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{
"title": "2016_000359e9029defe205a48885c3102e6a.pdf"
}
|
4
Abstract
In France, lengthening life expectancy forecasts an increase of the dependency phenomenon
for the future decades.
This dissertation presents first the definition of dependency, the different ways of evaluating
the level of senior’s dependency and the different assistance offered by government
and private insurances in order to finance the loss of autonomy. This part enables to
understand perspectives and stakes related to aging of the population.
The aim of this dissertation is to develop compartmental laws of policyholders, termination
and partial retention, having created beforehand a reliable database, in order to mesure the
impact on provisioning.
The estimation of exit’s gross rate has been made through Hoem’s likelihood estimation. The
|
1
|
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] |
{
"title": "2016_000359e9029defe205a48885c3102e6a.pdf"
}
|
choice of this estimator enables to calculate the exact exit risk exposure of a policyholder.
The reached rates have been sharpened by age groups, then smoothed by the Whittaker-
Henderson average.
This laws have been integrated in the forecast model of S2 Dependence of Predica
(Prophets). Moving to partial guarantees retention is possible and would have been
previously modeled as well as all the linked flows.
Then, we compared the different flows trajectories between the new and the former model,
namely the one that does not allow the transition to partial retention throughout the
projection. Afterwards, we proceeded to tendency study in the partial retention rates given
that the started tariff revision process could have an impact on the policyholders behaviour.
|
10
|
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{
"title": "2016_000359e9029defe205a48885c3102e6a.pdf"
}
|
conserver une garantie réduite en cas d’entrée en dépendance.
Lissage des taux bruts
Les taux bruts de sorties ont ensuite été lissés par la méthode de Whittaker-Henderson.
Cette méthode repose sur la combinaison d’un critère de fidélité et d’un critère de régularité
et d’en rechercher les valeurs ajustées qui minimisent la somme des deux critères, obtenue
par :
Avec et des paramètres du modèle.
Majoration de lois
Afin de mesurer l’impact de la révision tarifaire sur le comportement des assurés et ainsi de
mener une étude de sensibilité sur la déformation du portefeuille, nous déterminons un taux
de majoration à appliquer sur les taux de sortie en cas de révision tarifaire. L’unique année
|
100
|
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{
"title": "2016_000359e9029defe205a48885c3102e6a.pdf"
}
|
Un individu peut bénéficier de l’APA sous conditions, d’avoir 60 ans ou plus, de résider en
France et d’être en perte d’autonomie, c’est-à-dire évaluée par une équipe médico-sociale à
l’aide de la grille AGGIR dont le degré de dépendance est classé dans l’un des groupes 1 à 4.
L’état de dépendance partielle GIR 4 a été introduit par la nouvelle loi.
Si l’individu remplit ces critères, il peut toucher l’APA quel que soit son revenu. Cependant le
montant mensuel perçu dépend du revenu mais aussi de la nature de sa demande si c’est à
domicile ou en établissement.
De plus l’APA ne fait plus l’objet de récupération ni de son vivant, ni sur la succession, depuis
la promulgation de la loi de 2001.
L’APA à domicile :
|
1000
|
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{
"title": "2016_0385d80451de5c2ac868eb3227756a80.pdf"
}
|
quantitatives d’impact supplémentaires (QIS4 et QIS5) et spécifiques (LTGA) pour entrer
finalement en vigueur au 1er janvier 2016.
1.1. Une architecture à trois piliers
La Directive Solvabilité II est construite autour des trois piliers suivants :
Figure 1 – Solvabilité II : une architecture à trois piliersLe cadre réglementaire : la Directive Solvabilité II
Optimisation de la solvabilité de Swiss Life sous Solvabilité II
par des approches ALM sur le fonds euros, en environnement de taux bas
14/155
Le pilier I définit les exigences quantitatives, afin de déterminer les niveaux de capitaux
à détenir pour chaque compagnie et de calculer la couverture de cette exigence par les
fonds propres éligibles.
|
10000
|
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{
"title": "2016_3090fc160532a2ee243c3ca4be83d406.pdf"
}
|
Un deuxième théorème, le théorème central limite, permet de mesurer l’importance des fluctuations
auquel l’assureur fait face en fonction de la taille du portefeuille, lorsque celle-ci est assez grande.
En effet, le théorème stipule que, pour des variables indépendantes de même espérance ,
finie et de même variance , alors on a :
Avec étant la répartition d’une loi normale.
Pour plus de détails sur ces principes fondateurs de l’assurance, le lecteur est invité à consulter
l’article de CHARPENTIER (CHARPENTIER, 2001) qui revisite l’application de ces théories à
l’assurance.
B. Risque Systématique (risque non mutualisable)
Le paragraphe précédent partait du principe que d’une part, la population suivait un profil de
|
100000
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
physiques, cela revient simplement à répondre aux questions de l’assureur. Pour la
collectivité, il s’agit de décrire très précisément le risque qu’elle entend assurer et les
circonstances qu’elle connait déjà. Cette description sert de base à l’évaluation des risques. Il
est souvent difficile pour une collectivité d’évaluer les risques qu’elle encourt. Les raisons
peuvent être diverses et varient considérablement d’une structure à une autre. En fonction
de leur patrimoine, de leur implantation géographique (zones inondables, zones urbaines,
servitudes d’utilité publique…) ou bien encore de leur personnel, les collectivités ne sont pas
sur un pied d’égalité. C’est pourquoi elle se fera très souvent aider par un auditeur
|
100001
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
indépendant de toute compagnie d’assurance dans la rédaction d’un cahier des charges. Ce
cahier des charges préfigure le futur contrat d’assurance. En effet, sauf précisions de
l’assureur, c’est le cahier des charges qui fait office de contrat. Le dossier de consultation
comporte les conditions générales et les conditions particulières, propres à la collectivité et
établies après analyse des risques. Ceci permettra ainsi une couverture optimale de la
collectivité qui ne sera pas excessive et qui lui permettra de maîtriser son budget assurance.
La collectivité peut s’appuyer sur ses propres statistiques de sinistralité des dernières années
et ainsi identifier les points sur lesquels elle doit être vigilante. En cas de récurrence de
|
100002
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
certains sinistres de faible coût, il peut être envisagé une part d’autoassurance afin de
réintroduire une part d’aléa et de réduire les primes versées. A l’inverse, trop augmenter les
franchises pourrait déboucher sur une indemnisation à la marge des sinistres. Il conviendra
ainsi de déterminer de façon précise dans le cahier des charges les garanties souhaitées et
pour quels montants. Ces montants ne doivent pas basculer dans les extrêmes. Ils ne doiventArbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 121 -
pas être excessifs (sur-assurance), ce qui entraînerait une augmentation inutile de la cotisation
|
100003
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}
|
ou la qualification de fraude. Ils ne doivent pas non plus être sous-estimés (sous-assurance),
ce qui pourrait causer certaines déconvenues en cas de sinistres. En effet, il existe une règle
dite proportionnelle de prime ou de capitaux. Par exemple, il y a application de la règle
proportionnelle de capitaux lorsque la valeur assurée est inférieure à la valeur réelle. Dans ce
cas, l’assuré n’est indemnisé que dans la proportion du capital assuré par rapport à la valeur
réelle (montant des dommages*(valeur assurée/valeur réelle)). Le cahier des charges est
généralement communiqué à l’ensemble des assureurs qui sont libres de se porter candidats
ou non. Il comporte généralement les éléments suivants.
Le recensement du patrimoine de la collectivité
|
100004
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
Le recensement du patrimoine de la collectivité
Comme vu précédemment, c’est un point crucial à toute définition des besoins. Etablir un
inventaire exhaustif de ses biens apparaît comme une étape indispensable. Sous-évaluer son
patrimoine entraînerait une perte financière en cas de sinistre, et à l’inverse, le surévaluer
augmenterait inutilement les cotisations.
L’évaluation des risques
Une évaluation des risques doit être jointe à la consultation lancée par la collectivité. Cette
évaluation reprend, entre autres, les activités et autres compétences exercées par la
collectivité, le budget, la masse salariale, les bâtiments avec leurs surfaces, la flotte
automobile, et ce, afin de permettre à l’assureur d’effectuer une tarification au plus juste.
|
100005
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
La définition des risques assurés
Il s’agit de définir précisément l’objet du contrat (risque incendie, chute de la foudre, bris de
glace, risque RC automobile, etc.).
Les exclusions de garantie
Le contrat d’assurance contient des exclusions de garanties. Ces exclusions constituent les
risques non couverts par l’assureur. Elles peuvent être d’origine légale ou conventionnelle.Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 122 -
C’est à l’assureur, en cas de sinistre, de prouver l’exclusion. Le Code des assurances prévoit
des exclusions. En assurances IARD par exemple, la faute intentionnelle ou dolosive de
|
100006
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
l’assuré, la guerre étrangère, etc. sont exclues.
Les montants de garantie
La limite contractuelle d’indemnité est le montant, fixé d’un commun accord entre un assuré
et son assureur, et mentionné aux conditions particulières, au-delà duquel les dommages
assurés résultant d’un événement garanti ne sont plus pris en compte dans le calcul de
l’indemnité due par les assureurs au titre du contrat. Au sein de cette limite, le contrat prévoit
en général, des sous- limitations : une limite contractuelle à 15 000 000 euros, par exemple,
avec une sous-limitation pour le bris des glaces à 50 000 euros. Le montant de garantie
correspond à la somme maximale pouvant être perçue par l’assuré dans le cadre d’un sinistre
|
100007
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
donné. Ce montant peut être stipulé par sinistre, par événement et/ou par année d’assurance.
Il est exprimé en euros ou comme un multiple d’un indice de référence. Par exemple, pour
l’assurance des biens, le montant de garantie d’un sinistre peut être exprimé comme un
multiple de l’indice FFB (Fédération française du bâtiment).
La ou les franchises
Il existe une franchise dans la plupart des contrats d’assurance. La franchise correspond à la
somme qui reste à la charge de l’assuré en cas de réalisation du risque. Ainsi, lorsque le
montant du sinistre est inférieur à la franchise, l’assuré se trouve, de façon contractuelle, en
autoassurance.
La franchise peut s’exprimer par sinistre (à chaque fois que le sinistre se réalise, la franchise
|
100008
|
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-0.026746580377221107,
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
est appliquée) ou par année d’assurance (la franchise s’applique une seule fois sur l’ensemble
des sinistres d’une année). Par exemple, en assurance de dommages aux biens, la franchise
peut être exprimée en montant par sinistre. Dans ce cas, l’assureur n’interviendra qu’au-delà
de ce montant. Mais la franchise peut aussi être exprimée en montant cumulé sur une année.
Dans ce cas, quel que soit le nombre de sinistres, lorsqu’un certain montant est atteint,
l’assureur prend tout ce qui excède ce montant à sa charge.Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 123 -
|
100009
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
- 123 -
La franchise peut être absolue ou relative. La franchise absolue est toujours déduite du
montant du dommage. La franchise peut s’exprimer en montant ferme, en multiple d’un
indice ou en pourcentage de l’indemnité. Une pratique fréquente consiste à prévoir un
pourcentage (10 %, 15 % voire 20 %) des dommages à la charge de l’assuré avec un minimum
et un maximum par sinistre et/ou par année d’assurance pour les risques les plus coûteux,
comme l’incendie, par exemple. La franchise est relative lorsqu’elle n’est déduite que si le
montant des dommages lui est inférieur ou égal. Les sinistres inférieurs ou égaux à la franchise
ne sont alors pas réglés mais tous ceux qui sont supérieurs à la franchise sont indemnisés.
|
10001
|
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{
"title": "2016_3090fc160532a2ee243c3ca4be83d406.pdf"
}
|
mortalité fixe au cours du temps, et que d’autre part ce profil était connu par l’assureur, même si des
fluctuations pouvaient se manifester. Or en réalité, ces points ne sont pas nécessairement vérifiés,
engendrant le cas échéant un risque dit systématique pour l’assureur.
1. Risque d’erreur de modèle
En rebondissant sur le paragraphe précédent, rien ne garantit que l’assureur ait choisi une table de
mortalité coïncidant exactement avec la mortalité de la population assurée. Effectivement, à la date
de souscription, il n’a à priori aucune information substantielle sur le profil de mortalité de la
population qu’il s’apprête à prendre en charge.
Ce risque est mécaniquement non mutualisable, car inhérent à chaque individu assuré : il apparaît de
|
100010
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
Le montant de la franchise permet de ne pas prendre en compte les sinistres peu coûteux, au
vu des frais de déclaration et de traitement de dossier, dans le cadre de la sinistralité.
Le montant de la franchise devra correspondre à la somme que la collectivité peut verser elle-
même en cas de réalisation du sinistre, pour les sinistres très coûteux. Pour les autres, qui se
réalisent souvent et qui coûtent moins cher, la collectivité devra prévoir leur réalisation, quasi
certaine, dans son budget. Ceci permettra de n’être assuré que sur les risques vraiment
aléatoires et coûteux et ainsi, de bénéficier d’un contrat d’assurance au juste prix pour la
collectivité. Certaines franchises sont, dans leur principe et dans leur montant, imposées par
|
100011
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
la loi, pour les catastrophes naturelles, par exemple.
La prime
Pour s’assurer contre un risque, la collectivité paye une prime/cotisation à l’assureur. Le calcul
de cette dernière s’effectue au regard de plusieurs éléments :
le risque assuré (assurance responsabilité, assurance des biens) ;
la sinistralité (l’objet, la fréquence et le coût des sinistres constatés aux cours des
quatre ou cinq années précédentes).Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 124 -
ANNEXE 3 : Description et qualité des variables explicatives
La catégorie juridique (le type de collectivité territorial)
Descriptif :
|
100012
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] |
{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
Descriptif :
Nous définissons le type de collectivité grâce à la nomenclature des catégories juridiques. Il
s’agit d’un répertoire officiel d'immatriculation des entreprises et des établissements qui a été
élaboré sous l'égide du comité interministériel SIRENE®. Cette nomenclature a une vocation
inter-administrative. Elle est également utilisée dans la gestion du Registre du Commerce et
des Sociétés.
En ce qui nous concerne, l’extrême détail de cette table n’apporte rien à la mise en place de
notre tarif. Il serait même dangereux d’utiliser ce niveau de précision sachant que certains
codes ne concernent que quelques collectivités ce qui s’avèrerait très insuffisant pour
l’obtention d’un tarif robuste et fiable. Des regroupements ont donc été nécessaires. Ces
|
100013
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
regroupements existent déjà et ont été établis sur la base d’une connaissance métier des
différents profils de risque et éprouvés depuis une dizaine d’exercices.
Deux variables complémentaires sont également utiles.
La première est le code « tranche habitant ». Il nous donne une information sur le
nombre d’habitant pour les collectivités qui sont des communes. Cette information est
indispensable car les risques pour une petite commune de 500 habitants ne sont en
rien comparables à ceux d’une ville comme Marseille par exemple. Nous retiendrons
donc 7 tranches de nombres d’habitants pour les catégories juridiques de type
« commune ».
La seconde variable concerne les catégories juridiques de type « association ». Elle
|
100014
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
permet de distinguer les associations qui emploient des salariés, qui sont donc très
structurées et plus exposées que les petites associations de quartier (type pétanque
ou mots croisés).Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 125 -
Les contraintes de souscription nous amènent à utiliser 23 regroupements distincts de
collectivités. Elles sont représentées en nombre de contrats sur la Figure 51. Comme
mentionné dans la première partie, le nombre de contrats annuels sur la période 2006-2012
s’élève à un peu plus de 66 000 pour les communes de moins de 2 500 habitants contre 74
|
100015
|
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{
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|
pour les conseils régionaux (« Régions »). Ce constat est tout à fait représentatif du marché
global des collectivités et montre bien la difficulté à mettre en place un tarif.
Figure 51: Répartition par type de collectivité (23) (période 2006-2012)
La Figure 51 apporte une information complémentaire sur les surfaces assurées par
regroupement de catégorie juridique. La surface assurée sur la période 2006-2012 est de près
de 200 millions de m² pour les HLM (Figure 52) pour 1 500 contrats (figure 51) alors que les
communes de moins de 2 500 habitants représentent 80 millions de m² pour 20 000 contrats.
0
2 000
4 000
6 000
8 000
10 000
12 000
14 000
16 000
18 000
20 000Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
|
100016
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
collectivités. M.PLISSON, B.ROSSARD
- 126 -
Ces deux graphiques laissent imaginer l’extrême hétérogénéité des patrimoines et donc de
l’exposition aux risques des différents types de collectivités.
Figure 52 : Surfaces assurées par type de collectivité (23) (période 2006-2012)
Qualité de la donnée :
Le code catégorie juridique est une donnée globalement bien renseignée lors de
l’enregistrement informatique. Des erreurs peuvent subsister car la liste officielle est
tellement détaillée qu’il est très laborieux de trouver la bonne catégorie qui est rarement
communiquée par la collectivité elle-même. Cependant, ce type d’erreur reste marginal.
|
100017
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1.13982093334198,
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] |
{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
En outre, deux phénomènes permettent d’atténuer ces risques d’erreur.
Le premier est dû à la compétence du souscripteur. Lors de l’enregistrement du
dossier, c’est la catégorie juridique qui va aiguiller le rédacteur du contrat sur le bon
tarif. Le souscripteur possède une connaissance des tarifs moyens de chaque
0
20
40
60
80
100
120
140
160
180
200
En millions de m²Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 127 -
catégorie. Par conséquent, il est facile pour lui de se rendre compte que la catégorie
juridique renseignée n’est pas exacte (un conseil général sous un code commune par
exemple).
|
100018
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
exemple).
Le deuxième apparait au moment des regroupements de catégories. Le regroupement
« association » est par exemple, tellement générique (car très détaillé dans la table
d’origine), qu’une association loi 1901 qui ne serait pas sur le bon code catégorie
juridique finira de toute façon dans la catégorie association.
Nous avons donc ici une variable de qualité et qui est de toute façon indispensable car les
patrimoines sont très hétérogènes d’une catégorie à l’autre. Elle devrait donc être
particulièrement discriminante et influencer fortement le tarif.
Le type activité (code activité)
Sur le même principe que le code catégorie juridique, il existe une nomenclature d'activités
|
100019
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
Française (code NAF) qui a été élaborée principalement en vue de faciliter l'organisation de
l'information économique et sociale et à des fins statistiques. Cette information existe dans
notre système d’information et serait d’une grande utilité, principalement pour les catégories
telles que les associations ou surtout les syndicats. En effet, les activités des syndicats sont
très variées (ordures ménagères, etc.) et orientent donc fortement son exposition au risque.
Cette donnée est malheureusement très mal renseignée car sans impact tarifaire
actuellement. Nous prévoyons cependant dans un avenir proche de la rendre obligatoire et
de la vérifier afin d’affiner le tarif que nous allons mettre en place.
Le type de bâtiment
Descriptif
|
10002
|
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{
"title": "2016_3090fc160532a2ee243c3ca4be83d406.pdf"
}
|
manière « systématique » à chaque tête assurée, et augmenter la taille du portefeuille serait sans
effet. Pour reprendre l’analogie avec le lancer de dé, ce serait par exemple le fait qu’on anticipe que
chaque lancer de pièce est équiprobable, alors qu’en réalité la pièce est biaisée. Contrairement au
cas précèdent, augmenter dans ce cas le nombre de lancers n’aurait pas d’incidence sur cette erreur
d’estimation.
L’hétérogénéité peut également, de manière plus subtile, provoquer ce risque. Effectivement,
l’assureur peut théoriquement avoir une estimation correcte du risque des assurés se trouvant sur le
marché, et faire sa tarification sur cette estimation. Or entre le moment où il effectue cette
|
100020
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
Le type de bâtiment
Descriptif
Le type de bâtiment est également une variable qui devrait fortement influencer le tarif. En
effet, les risques (en fréquence et davantage en coût) sont totalement différents entre uneArbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 128 -
église, un immeuble d’habitation ou un bâtiment administratif. Le coût de reconstruction suite
à un incendie sera par exemple bien plus élevé pour un monument historique classé que pour
un gymnase. La fonction du bâtiment est également déterminante. Un HLM est beaucoup plus
|
100021
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
consommateur de la garantie « dégât des eaux » du fait du nombre important d’appartements
alors que les équipements publics vont davantage être sujets au vandalisme.
Les codes dont nous disposons dans nos bases de données sont les suivants :
1 : administration
2 : enseignement
3 : socioculturel
4 : sport
5 : culte
6 : habitation
7 : industrie
8 : sanitaire
9 : ouvrages d’art et de génie civil
10 : autres
Comme pour la catégorie juridique, nous présentons ci-dessous la répartition des contrats par
type de bâtiment sur la figure 53 puis la répartition des surfaces assurées totales par type de
bâtiment sur la figure 54.Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
|
100022
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
collectivités. M.PLISSON, B.ROSSARD
- 129 -
Figure 53 : Répartition des contrats par type de bâtiments (période 2006-2012)
Figure 54 : Répartition des surfaces assurées totales par type de bâtiment (période 2006-2012)
Une première remarque concerne la part « autres ». Elle est relativement importante et
occupe près de 25% des types de bâtiments tant en nombre qu’en surface. De plus, en se
penchant précisément sur la pertinence de cette variable, nous nous sommes rapidement
aperçus qu’elle était inexploitable, même s’il est fort probable que l’administratif et
l’habitation (HLM) occupent des parts aussi importantes.
Qualité de la donnée :
|
100023
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
Qualité de la donnée :
Le fonctionnement par AOP a des conséquences fortes sur l’organisation de la société, dont
deux principales pour ce qui nous intéresse.
Administratif
Autres
Habitation
3
5
2
4
7
8
Administratif
Habitation
Autres
2
3
8
5
7 4Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 130 -
La première contrainte forte provient du fait que la durée d’un contrat suite à la
procédure de mise en concurrence est en moyenne de 4 ans. A chaque fin d’exercice,
ce sont environ 25% des contrats qui arrivent à terme, ce qui revient à dire que le
|
100024
|
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] |
{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
chiffre d’affaire peut potentiellement chuter de 25% d’un exercice à l’autre.
La deuxième contrainte forte réside dans le fait que 90% de ces contrats sont annuels
c’est-à-dire à effet au 1er janvier et que par conséquent les collectivités lancent toutes
leurs appels d’offre à peu près au même moment, en général à partir du mois de
septembre.
Ce mode de fonctionnement implique que le renouvellement du chiffre d’affaire se joue sur 4
mois. L’entreprise a donc tendance à privilégier la réactivité aux appels d’offre afin de
sécuriser le chiffre d’affaire de l’exercice suivant. Cette priorité à la réactivité se fait parfois au
détriment de la qualité des données recueillies. La variable « type de bâtiment » est affectée
|
100025
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
par ce type de fonctionnement. La liste des bâtiments est relativement bien saisie pour les
petites affaires qui ne passent pas par AOP. En revanche, pour les autres qui ont des
patrimoines plus importants, il a été décidé que ce patrimoine serait saisi sur une unique ligne
« ensemble du patrimoine » avec sa surface totale associée, dans un but évident de gain de
temps.
La qualité de la collectivité (le statut de propriétaire)
Descriptif :
Les collectivités comme les particuliers peuvent être :
locataires (L) de bâtiments appartenant à d’autres structures ;
propriétaires (P) des logements qu’elle loue à ses usagers ou administrés ;
ou tout simplement propriétaires et occupantes (PO) des bâtiments de la mairie dans
lesquels travaillent ses salariés.
|
100026
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
lesquels travaillent ses salariés.
Le Code civil rend le locataire responsable des dommages qu’il peut causer au bien du
propriétaire. Les risques supportés par un locataire ou un propriétaire occupant sont
relativement proches. On s’attend donc à des primes relativement similaires. En revanche, laArbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 131 -
prime du propriétaire sera bien moindre car la majeure partie du risque est déjà supportée
par le locataire. Il s’agit donc là encore d’une variable essentielle qui devra être intégrée par
la suite.
|
100027
|
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] |
{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
la suite.
Figure 55 : Répartition du nombre de collectivités en fonction du statut de propriétaire
Figure 56 : Répartition de la surface assurée en fonction du statut de propriétaire
Les collectivités sont très majoritairement propriétaires et occupantes de leur bâtiment
comme le montrent les figures 55 et 56. Elles peuvent être également propriétaires d’autres
biens sans notion « d’occupation » comme par exemple des ouvrages d’art ou de génie civil.
Dans une moindre mesure, elles peuvent également être locataires de bâtiments appartenant
à d’autres entités. Un conseil général peut par exemple mettre des locaux à disposition d’une
des communes de la région.
0
10 000
20 000
30 000
40 000
50 000
60 000
70 000
80 000
90 000
L
P
PO
0
200
400
600
800
1 000
1 200
|
100028
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
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En millions de m²Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 132 -
Qualité de la donnée :
Cette donnée sera inexploitable pour les mêmes raisons que celles évoquées sur le type de
bâtiment. Le détail des types de bâtiments assurés n’étant pas disponible dans le système
informatique, les attributs qui lui sont rattachés (comme la qualité de l’assuré) ne le sont pas
non plus. En raison de son importance, ce critère de tarification sera intégré à posteriori.
Le produit d’assurance (ou contrat d’assurance)
|
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|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
Le produit d’assurance (ou contrat d’assurance)
Nous entendons par produit, un contrat standard commercialisé pour une cible spécifique.
Nous en proposons actuellement 4.
Le produit n°1 est à destination des petites collectivités, principalement les communes de
moins de 2 500 habitants.
Les produits n°2 et 3 s’adressent davantage aux associations respectivement avec salariés
(associations gestionnaires) et sans salariés (associations non gestionnaires).
Le produit n°4 était à l’origine un contrat standard, mais il sert aujourd’hui de base à
l’élaboration des réponses aux AOP.
Figure 57 : Répartition du nombre de collectivités par type de contrat
0
10 000
20 000
30 000
40 000
50 000
60 000
70 000
80 000
Produit n°1
Produit n°2
Produit n°3
|
10003
|
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{
"title": "2016_3090fc160532a2ee243c3ca4be83d406.pdf"
}
|
tarification et le moment où les individus souscrivent effectivement à ce contrat, les assurés peuvent
procéder à un arbitrage en leur faveur, qui modifierait le profil de risque effectivement pris en charge
par l’assureur.81
Théoriquement, on peut considérer que ce risque ne se présente pas à la souscription dans les
« articles 83 » car celle-ci est obligatoire à une catégorie objective de salarié. Cependant même dans
ce cas théorique, elle peut se présenter à la prorogation comme montré précédemment, du fait du
caractère optionnelle de la clause.
Un moyen d’estomper en partie ce risque est d’effectuer une tarification prudente en surévaluant le
risque moyen, par exemple via une prime de risque supplémentaire.
2. Risque de dérive de mortalité
|
100030
|
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] |
{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
60 000
70 000
80 000
Produit n°1
Produit n°2
Produit n°3
Produit n°4Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 133 -
Figure 58 : Répartition de la surface assurée par type de contrat
Les figures 57 et 58 montrent que le produit n°4 est clairement le plus représenté aussi bien
en nombre qu’en surface assurée puisqu’il est utilisé lors de toutes les réponses aux appels
d’offre. Les autres produits sont bien représentés en nombre mais beaucoup moins en
surface, car destinés à des structures plus petites. Il est quasi certain que cette variable sera
|
100031
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
fortement corrélée à la catégorie juridique de l’assuré. Nous la retenons tout même pour
l’instant car elle va nous permettre de déterminer les franchises.
L’origine de l’affaire (AOP ou non)
Nous entendons par origine de l’affaire le fait de savoir si le contrat résulte d’un AOP ou non.
Le constat est toujours le même. D’un côté, les petites collectivités (communes de moins de
2 500 habitants et associations) très nombreuses mais n’étant pas soumises à l’obligation de
mettre en concurrence les assureurs via un AOP et de l’autre les structures moins nombreuses
mais aux patrimoines beaucoup plus importantes (HLM, conseils généraux) qui sont
contraintes de passer par une procédure d’AOP, ce que montrent les figures 59 et 60.
0
200
400
600
800
1 000
1 200
1 400
1 600
|
100032
|
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] |
{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
0
200
400
600
800
1 000
1 200
1 400
1 600
Produit n°1
Produit n°2
Produit n°3
Produit n°4
En millions de m²Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 134 -
Figure 59 : Répartition du nombre de collectivités en fonction de la procédure d’appel d’offre
Figure 60 : Répartition de la surface assurée en fonction de la procédure d’AOP
Cette variable est de bonne qualité mais on peut raisonnablement penser qu’elle sera
fortement corrélée au type de collectivité.
Les franchises
Dans le système informatique, les franchises sont renseignées pour quatre garanties
|
100033
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
uniquement : l’incendie, le dégât des eaux, le vol et la tempête. Elles sont relativement bien
renseignées pour les franchises fixes, mais difficilement exploitables pour les autres types de
franchise. Pour les petites collectivités, elles ne sont pas renseignées. C’est alors la variable
« produits » qui va nous donner l’information. Nous avons également supprimé des bases
0
20 000
40 000
60 000
80 000
100 000
120 000
140 000
AO
HAO
0
200
400
600
800
1 000
1 200
1 400
1 600
AO
HAO
En millions de m²Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 135 -
|
100034
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
- 135 -
toutes les franchises marginales du type franchises annuelles, pour ne nous focaliser que sur
les franchises fixes.
Figure 61 : Répartition des collectivités par type de franchise
Figure 62 : Répartition de la surface assurée par type de franchise
Les figures 61 et 62 montrent que ce sont les plus grosses structures qui choisissent les
franchises les plus élevées, parfois jusqu’à 15 000€, ce qui semble logique.
Après plusieurs essais de modélisation, cette variable donne des résultats surprenants qui
n’ont aucune logique assurantielle. Les franchises les plus faibles donnent les tarifs les plus
faibles. Une autre solution envisagée aurait été de remettre tous les sinistres de nos bases de
|
100035
|
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] |
{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
données en franchise 0, c’est-à-dire d’ajouter la franchise à chaque sinistre ou celle-ci a été
déduite. Malheureusement la franchise appliquée à chaque sinistre n’est pas disponible dans
les bases.
0
10 000
20 000
30 000
40 000
50 000
60 000
70 000
80 000
90 000
0
100
200
300
400
500
600
En millions de m²Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 136 -
Cette variable ne sera donc pas retenue dans la modélisation. Il sera cependant indispensable
de l’ajouter par la suite pour différencier nos tarifs selon les niveaux de franchise. Nous
|
100036
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
considérerons que le tarif obtenu correspond à une franchise moyenne du portefeuille que
nous déclinerons ensuite par tranche à l’aide d’études de distributions des coûts de sinistre.
Le zonage des différentes aires urbaines
Cette variable est une variable externe dans le sens où elle n’est pas directement disponible
dans nos bases de données. L’objectif de ce zonage est de mieux apprécier le risque lié à la
situation géographique de la collectivité : rural, périurbain ou urbain. En effet, nous percevons
aisément que les risques supportés par les communes très urbanisées sont différents de ceux
d’une commune de même taille mais située hors agglomération (on évite d’intégrer une
variable qui serait redondante avec la taille de la commune). On pense aux garanties de
|
100037
|
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] |
{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
vol/vandalisme notamment, mais on peut aussi penser que cette variable remplacera plus ou
moins le manque de détail du patrimoine assuré.
Construction de la table de zonage :
Nous sommes partis d’une table disponible sur le site internet de l’INSEE classant les
communes (à partir de leur code INSEE) en différentes aires urbaines. Les définitions de
l’INSEE sont mentionnées ci-dessous :
« Une aire urbaine ou "grande aire urbaine" est un ensemble de communes, d'un seul tenant
et sans enclave, constitué par un pôle urbain (unité urbaine) de plus de 10 000 emplois, et par
des communes rurales ou unités urbaines (couronne périurbaine) dont au moins 40 % de la
population résidente ayant un emploi travaille dans le pôle ou dans des communes attirées par
celui-ci.
|
100038
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
celui-ci.
Le zonage en aires urbaines 2010 distingue également :Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 137 -
- les "moyennes aires", ensemble de communes, d'un seul tenant et sans enclave, constitué par
un pôle (unité urbaine) de 5 000 à 10 000 emplois, et par des communes rurales ou unités
urbaines dont au moins 40 % de la population résidente ayant un emploi travaille dans le pôle
ou dans des communes attirées par celui-ci.
- les "petites aires", ensemble de communes, d'un seul tenant et sans enclave, constitué par un
pôle (unité urbaine) de 1 500 à 5 000 emplois, et par des communes rurales ou unités urbaines
|
100039
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
dont au moins 40 % de la population résidente ayant un emploi travaille dans le pôle ou dans
des communes attirées par celui-ci. »22
Le nombre de modalités de la variable étant trop importante (9) dans la table INSEE, nous
avons préféré en réduire le nombre pour arriver aux 4 suivantes :
zone URBAINE_Niv1 : ( sur la carte ci-dessous, figure 63) : ce sont les communes
appartenant à un grand pôle (10 000 emplois ou plus) ;
zone URBAINE_Niv2 : ( sur la carte ci-dessous) : ce sont les communes appartenant
à un pôle « aires moyennes » (5 000 à moins de 10 000 emplois) ;
zone PERIURBAINE : ( sur la carte ci-dessous) => ce sont les communes appartenant
à la couronne d'un grand pôle ;
|
10004
|
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{
"title": "2016_3090fc160532a2ee243c3ca4be83d406.pdf"
}
|
2. Risque de dérive de mortalité
Un autre type de risque peut se matérialiser concernant le comportement plus général de la
mortalité du portefeuille. En effet, jusqu’à présent on sous entendait que cette mortalité, connue ou
pas, était fixe au cours du temps. Mais des études (CAIRNS, et al., 2004) montrent que le profil de
mortalité peut lui-même être aléatoire, ce qui engendre un nouveau risque non systématique : on
parle alors de mortalité stochastique. Comme dans le cas précédent, ce risque ne peut pas se
mutualiser avec la taille du portefeuille.
En reprenant à nouveau l’analogie avec les 100 lancers, ce serait le risque qu’entre deux séries de
100 lancers, les probabilités de tomber sur « face » ou « pile » de la pièce soient déterminées de
manière aléatoire.
|
100040
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
à la couronne d'un grand pôle ;
zone RURAL : ( sur la carte ci-dessous) => ce sont les communes appartenant à un
petit pôle (de 1 500 à moins de 5 000 emplois), à la couronne d'un petit ou moyen pôle
avec des communes isolées hors influence des pôles.
Pour une meilleure visualisation de ces regroupements, nous les avons représentés sur la
figure 63.
22 https://www.insee.fr/fr/metadonnees/definition/c2070Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 138 -
Figure 63 : Répartition des différentes zones urbaines
|
100041
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
Figure 63 : Répartition des différentes zones urbaines
Une autre variable que nous souhaitons prendre en compte est l’activité touristique de la
commune. Les stations balnéaires et surtout les stations de ski ont des équipements très
spécifiques du type « remontées mécaniques » par exemple, qui suite à une avalanche
peuvent se révéler très couteux pour l’assureur tant dans l’indemnisation du bien que dans
celles des pertes d’exploitation en pleine période scolaire. Par exemple, la chute du pilonne
d’une remontée mécanique peut entraîner un manque à gagner important pour la station deArbitrage entre mutualisation et segmentation : le cas des assurances dommages de
|
100042
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
collectivités. M.PLISSON, B.ROSSARD
- 139 -
sport d’hiver. Ces équipements peuvent d’ailleurs appartenir à une commune ou à un syndicat
intercommunal.
Le site de la Direction Générale des Entreprises (DGE) nous indique si une commune est
touristique ou non. Les données et analyses qui suivent s’appuient sur le dispositif statistique
national du tourisme, auquel la DGE contribue, en partenariat avec l’INSEE, la Banque de
France (balance des paiements) et les partenaires territoriaux. Cette table est représentée sur
la figure 64.
Figure 64 : Cartographique des lieux touristiquesArbitrage entre mutualisation et segmentation : le cas des assurances dommages de
|
100043
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
collectivités. M.PLISSON, B.ROSSARD
- 140 -
Sans surprise, ce sont clairement les zones littorales (sud-ouest notamment) et zones
montagneuses (Alpes et Pyrénées) qui ressortent.
Cette table sera donc croisée avec la précédente et donne les répartitions illustrées sur les
figures 65 et 66.
Figure 65 : Répartition des collectivités en fonction des différentes zones urbaines
Figure 66 : Répartition de la surface assurée en fonction des différentes zones urbaines
Afin de contrôler la représentativité de notre portefeuille, nous vérifions que la répartition
des collectivités en fonction des différentes zones urbaines reste très proche de ce que nous
|
100044
|
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] |
{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
pouvons constater sur la France entière (figure 67).
0
5 000
10 000
15 000
20 000
25 000
30 000
35 000
40 000
45 000
50 000
0
100
200
300
400
500
600
700
800
900
1 000
En millions de m²Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 141 -
Type de zone urbaine
Répartition des collectivités
au niveau national
Répartition des collectivités
assurées par la compagnie
URBAIN_niv1
9%
31%
URBAIN_niv2
1%
3%
PERIURBAIN
44%
36%
RURAL
46%
30%
Figure 67 : Répartition des collectivités par type de zone urbaine
On observe un décalage important concernant la modalité « Urbain_niv1 ». Nous attribuons
|
100045
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
ce décalage à un phénomène que nous n’avons pas évoqué mais qu’il est important de garder
à l’esprit. La répartition nationale est basée uniquement sur les 37 000 communes françaises,
donc sur la catégorie juridique « commune ». Or dans notre portefeuille nous avons une
multitude d’autres types de collectivités. Si nous prenons l’exemple des conseils régionaux,
ces derniers n’apparaissent pas dans la répartition nationale alors que dans notre portefeuille
ils sont affectés au code INSEE de la ville dans laquelle se situe le siège. C’est pourquoi toutes
ces structures (autres que communes) vont se retrouver dans la modalité « Urbain_niv1 » et
c’est ce qui explique en partie ce décalage par rapport à la répartition nationale des
|
100046
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
communes.Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 142 -
ANNEXE 4 : Quel historique retenir ?
Le montant des provisions
Il apparaît indispensable de ne pas construire notre tarif sur des exercices récents constitués
par des provisions encore très élevées. Un montant de provisions trop élevé nuit à la qualité
de la charge de sinistre finale. D’autant plus qu’une autre spécificité de l’assurance des
collectivités est la gestion des indemnisations. Pour les garanties de masse telles que le « bris
de glace » ou le « dégât des eaux », les déclarations et le paiement du sinistre se font
|
100047
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
généralement très rapidement. Il existe cependant une quantité non négligeable d’assurés qui
devant le nombre élevé de sinistres annuel (parfois plus de 1 000 par an) mentionnent au
contrat que les déclarations se feront trimestriellement. Cependant, ceci n’influe guère sur le
niveau de provisions car ces sinistres sont en général réglés 6 mois après la clôture de
l’exercice. Ce qui modifie davantage le volume de provision est l’incertitude élevée qui pèse
sur le montant à indemniser des sinistres graves en incendie. A la différence de l’assurance de
particulier, du fait de l’immense diversité des patrimoines, chaque sinistre grave présente des
caractéristiques propres. Généralement, les délais d’indemnisation sont très longs pour les
raisons suivantes.
|
100048
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
raisons suivantes.
1. Le bâtiment sinistré doit être expertisé mais la sécurisation de l’accès est parfois
laborieuse, et l’expertise, notamment dans le cas de monuments historiques, peut
durer plusieurs mois.
2. Face à un sinistre, la collectivité a en général deux options. Soit elle fait reconstruire à
l’identique ce qui peut durer parfois plusieurs années et le provisionnement évolue
alors jusqu’à l’achèvement des travaux. Soit elle fait reconstruire un autre type de bien
(un parking à la place d’un gymnase par exemple) et doit alors lancer des appels d’offre
pour trouver les sociétés intéressées. Dans les deux cas, les délais d’indemnisation sont
rallongés.
3. Un dernier facteur d’importance est le positionnement du recours. Dans le cas d’un
|
100049
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
incendie criminel par exemple, la procédure est très longue. Il faut d’abord que le tiersArbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 143 -
soit identifié puis jugé responsable et surtout solvable, ce qui peut parfois prendre
jusqu’à 5 ans.
En juin 2015, les provisions sur la charge de l’exercice 2014 s’élèvent à 50%, à 20% sur 2013
et 5% sur 2012. Nous ne retiendrons donc pas les exercices 2013 et 2014, sachant que 5% en
2012 additionné à des exercices liquidés rajoute peu d’incertitude sur la charge définitive
totale. Nous nous arrêterons donc en 2012.
La stabilité du portefeuille dans le temps
|
10005
|
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{
"title": "2016_3090fc160532a2ee243c3ca4be83d406.pdf"
}
|
manière aléatoire.
C. Formalisation du solde technique et financier
Précédemment, il a été étudié la projection du compte du fonds de rente dans différents cas de
rentes viagères, mais à chaque fois dans un cadre où les hypothèses économiques et de mortalités
fixées ex ante étaient scrupuleusement respectées (projections déterministes).
Or en pratique, des écarts se manifestent entre ce qui est anticipé et ce qui est constaté. Néanmoins,
l’assureur évalue ses soldes d’ouverture et de fermeture du compte de rente d’un contrat comme s’il
n’y avait pas eu d’écarts. Ainsi, ces écarts doivent être comptabilisés pour compenser ces évaluations
faites à l’ouverture et à la fermeture : c’est ce que reflète le solde technique et financier, à savoir le
résultat du fonds de rente.
|
100050
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
La stabilité du portefeuille dans le temps
Un deuxième élément fondamental pour la qualité du tarif est de disposer d’un historique sur
lequel la composition du portefeuille est la plus stable possible. Les figures 68, 69 et 70 nous
montrent l’évolution des principales variables explicatives sur la période 2001-2012.
Figure 68 : Composition relative par zones urbainesArbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 144 -
Figure 69 : Composition relative par type de collectivités
Figure 70 : Composition relative par niveau de franchise
|
100051
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
Figure 70 : Composition relative par niveau de franchise
La période 2001-2005 correspond au développement du portefeuille qui a été multiplié par 3
sur cette période. C’est d’ailleurs sur ces exercices que l’on constate le plus de disparités. A
partir de 2006 on observe une certaine stabilité. En outre, aucune évolution majeure n’est à
retenir sur cette période concernant la législation. Pas de fusions de régions ou de
départements. La revalorisation s’effectuera à partir de cette longueur d’historique
(quatrième partie).Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 145 -
La taille de la base de données
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100052
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
- 145 -
La taille de la base de données
Le fait de ne retenir que la période 2006-2012 nous permet de disposer de 300 000 sinistres
et d’une surface assurée cumulée de 1,6 milliards de m². Cette taille de base de données nous
semble suffisante pour établir un tarif significatif.Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 146 -
ANNEXE 5 : Quelles variables explicatives retenir ?
Nous allons donc regarder quelles variables ont un effet significatif sur la fréquence d’abord
puis sur le coût moyen ensuite pour chacune de nos quatre garanties à modéliser. Comme il
|
100053
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
s'agit de savoir si une variable quantitative (notre variable à expliquer : la fréquence) a des
valeurs significativement différentes selon les modalités d'une variable qualitative (nos
différentes variables explicatives) nous allons procéder à une analyse de la variance (ANOVA)
et utiliser le test de Fisher. L’objectif est de déterminer si les variables explicatives ont un effet
significatif sur les variables à expliquer ou si la variation de la variable expliquée s’explique par
des erreurs aléatoires ui. Dans un deuxième temps nous vérifierons que les variables
explicatives retenues dans la première partie sont suffisamment indépendantes.
L’ANOVA : Principe et hypothèses
Nous voulons démontrer dans cette première partie que nos variables explicatives (la
|
100054
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
catégorie juridique de l’assuré, le produit, la zone…) ont un effet sur la fréquence et le coût
moyen espérés des dossiers sinistre. Autrement dit, nous souhaitons comparer la moyenne
(variable quantitative) de chacun des échantillons (variable qualitative).
Le principe est celui de la décomposition de la variance (intra-classe et interclasse). L’ANOVA
utilise le mécanisme du F de Fisher non pas pour comparer deux variances d’échantillons mais
bien les deux composantes d’une même variance. Nous retiendrons donc les hypothèses
suivantes
H0 : « les moyennes sont égales » ;
contre H1 : « au moins deux moyennes sont différentes ».
Les hypothèses préalables à la mise en place d’une ANOVA sont les suivantes :
|
100055
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
Normalité et homoscédasticité des échantillons de chaque modalité ;
Indépendance entre les échantillons.Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 147 -
L’hypothèse de normalité est discutable. Elle n’est cependant pas irréaliste étant donné la
taille de chacun des échantillons (au moins 1 000 observations). En effet, le théorème central
limite garantit la normalité asymptotique des moyennes empiriques.
L’hypothèse d’indépendance de chacun des échantillons semble raisonnable dans la mesure
où il s’agit de la garantie incendie, qui n’est pas une garantie type « évènements climatiques »
|
100056
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{
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|
touchant plusieurs bâtiments simultanément. Certes, un incendie peut toujours se propager
dans les bâtiments de la mairie et détruire les locaux d’une association hébergée par cette
même mairie. Cependant, ces cas de figures sont trop rares pour perturber l’indépendance de
nos échantillons. Enfin il reste à vérifier l’homogénéité des variances (homoscédasticité) de
chacun des échantillons. Pour cela, nous avons réalisé un test d’homogénéité des variances
sous SAS.
Les variables explicatives de la fréquence de l’incendie
Nous essayons ici de déterminer quels sont les variables explicatives pertinentes.
Le type de collectivité a-t-il un effet sur la fréquence ?
Nous avons réalisé ce test à l’aide du logiciel SAS en testant les hypothèses présentées
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100057
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
précédemment. Ici, la probabilité critique associée au test de Fisher est inférieure à 5% donc
nous rejetons H0 avec une probabilité de se tromper < 0.01%. La variable « type de
collectivité » est donc retenue.Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 148 -
La fréquence est donc significativement différente selon la catégorie juridique de la
collectivité. Ce résultat semble logique dans la mesure où la fréquence du sinistre incendie est
naturellement différente entre une association louant un local et un conseil régional.
Le produit a-t-il un effet sur la fréquence ?
|
100058
|
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] |
{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
Le produit a-t-il un effet sur la fréquence ?
La probabilité critique associée au test de Fisher est inférieure à 5%. Il y a donc une différence
significative entre les fréquences de chaque produit. La variable produit est donc retenue dans
notre modèle.
L’origine de l’affaire (AOP/HAOP) a-t-elle un effet sur la fréquence:
Ici, la probabilité critique associée au test de Fisher est supérieure à 5%. Nous ne pouvons
donc pas rejeter H0. Cette variable ne semble donc pas exercer d’influence sur la fréquence
du sinistre en incendie. La variable « origine de l’affaire » ne sera donc pas intégrée au modèle.
Le fait que cette variable n’apporte pas d’information est somme toute logique. En effet, une
|
100059
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
structure non soumise à la contrainte du Code des marchés publics a le choix entre s’assurer
directement ou lancer un AOP, mais le risque sous-jacent reste exactement le même.
Le zonage a-t-il un effet sur la fréquence ?Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 149 -
La probabilité critique associée au test de Fisher est inférieure à 5%. Il y a donc une différence
significative entre les fréquences de chaque zone urbaine. La variable « zonage » est donc à
retenir. Ce résultat justifie également le choix d’avoir retenu cette table de zonage et valide
|
10006
|
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{
"title": "2016_3090fc160532a2ee243c3ca4be83d406.pdf"
}
|
résultat du fonds de rente.
En particulier, un solde positif suppose que les écarts sont favorables pour l’assureur, menant à un
profit : le Code des Assurances impose alors à l’assureur de redistribuer une grande partie de ce
profit aux rentiers sous forme de revalorisation de rente.
A l’inverse, un solde négatif suppose des écarts défavorables alors comptabilisés comme perte pour
le régime : ce solde est alors reporté à l’exercice suivant, dans l’espoir d’être compensé par un profit
futur. Si au terme du contrat le solde est toujours négatif, cette perte sera alors au titre de l’assureur
du fait de son engagement de couvrir le risque viager.
Ces soldes reflètent donc l’état financier du régime, ainsi que la bonne gestion ou non des risques par
|
100060
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
le fait que la probabilité d’avoir un incendie dans une grande ville n’est pas la même que dans
un petit village du fait d’un environnement totalement différent : délinquance, centre de
secours plus proche, etc.
Les variables explicatives du coût moyen de l’incendie
Le type de collectivité a-t-il un effet sur le coût moyen ?
La probabilité critique associée au test de Fisher est inférieure à 5%. Il y a donc une différence
significative entre les coûts moyens de chaque type de collectivité. La variable « type de
collectivité » est donc à retenir. Là encore, ce résultat semble naturel tant le coût de l’incendie
d’une église est différent de celui d’un gymnase.
Le produit a-t-il un effet sur le coût moyen ?
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
Le produit a-t-il un effet sur le coût moyen ?
La probabilité critique associée au test de Fisher est supérieure à 5%. Les coûts moyens ne
sont pas significativement différents d’un produit à l’autre. Cette variable n’est donc pas à
retenir.Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 150 -
L’origine de l’affaire (AOP/HAOP) a-t-elle un effet sur le coût moyen ?
La probabilité critique associée au test de Fisher est inférieure à 5%. Les coûts moyens sont
significativement différents selon qu’il s’agit d’un AOP ou non. Cette variable est donc à
retenir.
Le zonage a-t-il un effet sur le coût moyen ?
|
100062
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
Le zonage a-t-il un effet sur le coût moyen ?
La probabilité critique associée au test de Fisher est nettement inférieure à 5%. Les coûts
moyens sont significativement différents selon la zone du bâtiment. Cette variable est donc à
retenir.
Les variables retenues
Les différents tests réalisés suggèrent de retenir pour la garantie incendie :
le type de collectivité, le produit et le zonage pour la fréquence ;
le type de collectivité, l’origine et le zonage pour le coût moyen.
Ces mêmes tests ont été réalisés sur les 3 autres garanties à modéliser. Les résultats sont tous
équivalents aux précédents. Nous retiendrons donc à ce stade de l’étude et pour l’ensemble
des garanties :
|
100063
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
des garanties :
le type de collectivité, le produit et le zonage pour la fréquence ;Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 151 -
le type de collectivité, l’origine et le zonage pour le coût moyen.
Corrélation entre variables explicatives
Il convient maintenant d’étudier l’indépendance de nos variables explicatives. Nous étudions
ici le lien statistique entre plusieurs variables qualitatives prises deux à deux. Nous utiliserons
pour cela le V de Cramer qui a l’avantage par rapport au test du χ² d’être normalisé entre 0 et
1. Sa formule s’écrit de la manière suivante :
ܸ ൌ ඨ
߯²
߯²݉ܽݔ ൌ ඨ
߯²
|
100064
|
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] |
{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
ܸ ൌ ඨ
߯²
߯²݉ܽݔ ൌ ඨ
߯²
݊ ∗ ሾminሺ݈, ܿሻ െ 1ሿ
Avec :
n : effectif total ;
l et c : respectivement nombre de lignes et de colonnes du tableau de contingence.
Les hypothèses d’application de ce test sont les mêmes que celles du khi-deux à savoir :
indépendance des observations ;
les fréquences attendues (espérées) ne doivent pas être petites ;
toutes les réponses doivent être incluses dans le tableau, pour prendre en
considération toutes les variables.
Ces hypothèses, peu contraignantes en général, sont entièrement remplies dans notre cas.
L’indépendance des observations est acquise pour les mêmes raisons que pour l’ANOVA et le
grand nombre d’observations fait qu’aucune fréquence attendue n’est trop petite.
|
100065
|
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0.6016424894332886,
-0.17758828401565552,
0.007297005504369736,
0.5040593147277832,
0.6561973094940186,
0.0840669497847557
] |
{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
Nous rappelons également que plus V est proche de zéro, plus il y a indépendance entre les
deux variables étudiées. Il vaut 1 en cas de complète dépendance puisque le χ² est alors égal
au χ² max. Nous nous appuierons sur l’échelle suivante pour l’arbitrage de nos
résultats présentée dans la figure 71.Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 152 -
Figure 71 : Echelle des niveaux de corrélation
Nous avons donc, pour chacune des quatre garanties, réalisé le test de Cramer sur chacune
des variables explicatives prises deux à deux. Ces résultats sont présentés sous forme
synthétiques dans la figure 72.
|
100066
|
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] |
{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
synthétiques dans la figure 72.
Figure 72 : Synthèse des corrélations entre variables par garantie
Les résultats sont très similaires pour l’ensemble des garanties. Les résultats de la figure 72
indiquent que les variables « types de collectivité » et « produit » sont fortement corrélées.
Cette conclusion est logique car le produit dépend de la catégorie juridique. Il existe
notamment un produit pour les associations et un pour les communes de moins de 2 500
habitants. Cette variable ne peut être que corrélée au type de sociétaire. Concernant l’origine
Valeur
Force du lien statistique
0
Absence de relation
Entre 0,05 et 0,10
Très faible
Entre 0,10 et 0,20
Faible
Entre 0,20 et 0,40
Modérée
Entre 0,40 et 0,80
Forte
Entre 0.80 et 1
Quasi colinéarité
Garantie
INCENDIE
|
100067
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
Forte
Entre 0.80 et 1
Quasi colinéarité
Garantie
INCENDIE
Type
collectivité
Origine
Produit
Zonage
Type
collectivité
Origine
0.63
Produit
0.82
0.38
Zonage
0.28
0.28
0.30
Garantie
DEGAT DES
EAUX
Type
collectivité
Origine
Produit
Zonage
Type
collectivité
Origine
0.70
Produit
0.83
0.31
Zonage
0.34
0.25
0.18
Garantie
BRIS DE
GLACE
Type
collectivité
Origine
Produit
Zonage
Type
collectivité
Origine
0.64
Produit
0.85
0.28
Zonage
0.27
0.31
0.25
Garantie
VOL/VANDA
LISME
Type
collectivité
Origine
Produit
Zonage
Type
collectivité
Origine
0.68
Produit
0.89
0.26
Zonage
0.21
0.33
0.28Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
|
100068
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
- 153 -
de l’affaire (AOP ou HAOP), la remarque est semblable. Ce sont en effet les plus grosses
structures (conseils généraux, régionaux….) qui sont contraintes de lancer une consultation
alors que les plus petites (communes de moins de 2 500 habitants ou association) ne le sont
pas.
L’analyse statistique menée dans cette annexe nous a montré que sur l’ensemble des variables
disponibles, peu présentent les qualités suffisantes pour pouvoir être prises en compte dans
la construction du tarif. D’un autre côté, compte tenu de l’extrême hétérogénéité de
l’assurance des collectivités par rapport à celle des particuliers, il faut être conscient que
construire un tarif suffisamment segmenté pour répondre à l’ensemble des cas possibles
|
100069
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
nécessiterait un nombre bien trop important de variables explicatives. En poussant ce
raisonnement à l’extrême, ce nombre de variables pourrait être proche du nombre d’assurés
potentiels, ce qui serait aberrant. Ce sont ces considérations qui nous ont naturellement
amenés à utiliser la théorie de la crédibilité pour remplacer les variables explicatives
manquantes (voire inexistantes) par l’expérience propre de chaque assuré.Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 154 -
ANNEXE 6 : Validation du tarif GLM
Cette annexe présente les différents tests qui ont pu être menés pour nous assurer de la
|
10007
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{
"title": "2016_3090fc160532a2ee243c3ca4be83d406.pdf"
}
|
l’assureur : une bonne gestion est implicitement équivalente à des comptes équilibrés, c'est-à-dire
avec des résultats proches de zéro en moyenne, sans grosse variabilité.
Il est proposé dans cette section de s‘appuyer sur les relations de récurrence établies précédemment
pour formaliser l’évaluation des soldes techniques et financiers.82
Ces éléments serviront directement pour l’application numérique du cas pratique, consistant
justement à projeter les résultats d’un fonds de rente.
1. Dans le cas d’une Rente Viagère Immédiate
On considère le cas simplifié du fonds de rente d’une rente viagère immédiate telle qu’étudiée
précédemment, en tenant compte cette fois ci du fait que la mortalité réelle ne coïncide pas avec
l’anticipé.
|
100070
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
qualité et de la robustesse du tarif obtenu par la modélisation GLM. La première partie est
une approche générale qui vise à valider le modèle sur une base de validation d’abord puis
sur le portefeuille dans sa globalité sur deux exercices consécutifs. La deuxième partie teste la
robustesse du tarif, c’est-à-dire sur la sensibilité du tarif aux différents paramètres/arbitrages
qui ont été effectués tout au long de cette étude.
Nous rappelons que notre approche a consisté à modéliser un tarif par GLM sur une base de
données que nous avons nommée « base d’apprentissage » et qui représentait 60% de notre
échantillon global. Cette sélection a été faite de façon purement aléatoire. Les 40% restants
|
100071
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
représentent la « base de validation ». Cette approche est utile, quand la taille de l’échantillon
le permet, pour vérifier que les paramètres obtenus dans la modélisation GLM ne sont pas
sensibles à l’échantillon retenu. Dans un souci permanent de vérification de notre modèle,
nous ne nous sommes pas contentés d’utiliser cette « base de validation ». Nous avons
également appliqué notre modèle sur la « base d’apprentissage ». Cet exercice peut paraitre
trivial mais dont nous voulions nous assurer du résultat. Nous avons donc comparé les
nombres de sinistres et charges réels et estimé le tarif sur chacune des deux bases, au global
|
100072
|
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] |
{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
et par type de collectivités. Les résultats sont présentés sur la figure 73.Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 155 -
Figure 73 : Comparaison entre base d’apprentissage et base de validation
Les résultats obtenus à partir de la « base d’apprentissage » sont très satisfaisants. Aucun
écart important n’est à constater au global (en nombre de sinistres et en charge). Ceci nous
conforte sur les options retenues et l’absence d’éventuelles erreurs sur la mise en place du
modèle. Sur la « base de validation », le modèle est globalement bien ajusté aux données
|
100073
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
(entre 2% et 3% d’écart entre le réel et l’estimation). En revanche, en regardant les résultats
par types de collectivités, nous observons des disparités plus importantes. Les écarts les plus
importants s’observent sur les types de collectivités ayant peu d’observations (par exemple :
CCI +355% avec seulement 60 observations) mais également sur les types de structure les plus
importants (conseils généraux et régionaux, villes de plus de 40 000 habitants). Ce phénomène
s’explique par le fait que les structures les plus importantes ont leur propre comportement,
avec une sinistralité importante et récurrente et des programmes d’assurance souvent bien
spécifiques. Elles ne correspondent donc pas à un comportement standard que modélise une
|
100074
|
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] |
{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
approche GLM. Ces tarifs seront tout de même conservés, car c’est justement dans ces cas
précis que l’approche du tarif par la théorie de la crédibilité prend tout son sens. Cette
Type de collectivité
Nombre
d'observations
Ecart
nombre
Ecart
charge
Nombre
d'observations
Ecart
nombre
Ecart
charge
Association gest
9350
0%
4%
6259
9%
10%
Association non gest
3742
0%
5%
2535
11%
114%
Autres collectivites publiques
1676
0%
0%
1044
-6%
59%
CCAS
1360
0%
1%
904
15%
94%
CCI
94
0%
0%
60
137%
355%
Communautes d agglomeration
706
0%
0%
474
14%
1%
Communautes de communes
3362
0%
-1%
2204
6%
13%
Communautes urbaines
78
2%
2%
55
-9%
158%
Commune 7 000 / 15 000 hab
2110
-1%
0%
1368
3%
0%
Communes - 2 500 hab
39697
0%
0%
26588
-2%
8%
Communes 15 000 / 40 000 Hab
1022
0%
0%
632
-6%
-4%
|
100075
|
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] |
{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
-2%
8%
Communes 15 000 / 40 000 Hab
1022
0%
0%
632
-6%
-4%
Communes 2 500 / 5 000 hab
7585
1%
0%
5155
-2%
-12%
Communes 40 000 / 100 000 hab
303
0%
0%
202
-17%
-30%
Communes 5 000 / 7 000 hab
1944
0%
2%
1330
1%
33%
Communes de plus de 100 000 hab
65
0%
0%
26
34%
-40%
Departements
282
0%
0%
203
41%
1%
HLM
898
0%
0%
560
4%
11%
Marche des entreprises
953
1%
0%
636
4%
10%
Personnes morales de droit Prive
534
0%
18%
379
23%
-58%
Regions
47
0%
0%
27
4%
-26%
SDIS
86
0%
-1%
64
-1%
-6%
Structures hospitalieres
899
0%
1%
618
15%
11%
Syndicats
3012
1%
1%
1953
-10%
-41%
Global
79805
0%
0%
53276
2%
3%
Base d'apprentissage
Base de validationArbitrage entre mutualisation et segmentation : le cas des assurances dommages de
|
100076
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
collectivités. M.PLISSON, B.ROSSARD
- 156 -
première validation nous conforte donc sur la modélisation GLM. Cependant, les écarts parfois
importants montrent qu’un GLM seul n’est pas adapté à ce type de portefeuille.
La deuxième étape de validation consiste en un back-testing dont le but est de voir dans quelle
mesure le tarif généré par le modèle GLM diffère des tarifs actuellement proposés par la
société d’assurance. Plus précisément, nous allons d’abord regarder les écarts entre les
cotisations théoriques résultant du modèle et les cotisations réellement appelées sur
plusieurs exercices. Nous regarderons ensuite plus en détail la distribution des écarts par
assuré.
|
100077
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
assuré.
Afin de valider notre tarif dans sa globalité, nous l’avons donc appliqué sur l’ensemble de notre
base de données agrémentée des données 2010 à 2014. Les résultats de cette étude sont
présentés dans le tableau suivant par type de collectivité (figure 74).
Figure 74 : Comparatif tarif théorique / réel.
Globalement, les tarifs générés par l’approche GLM sont globalement supérieurs de 22% aux
prix de l’ensemble des affaires déjà en portefeuille. Nous précisons ici que la vision portefeuille
n’est absolument pas le reflet d’une quelconque politique tarifaire à un moment donné. En
Exercices 2010 à 2014
Ecart TARIF
S/C réel
S/C
théorique
Association gest
1,06
74%
69%
Association non gest
1,19
68%
57%
Communautes urbaines
0,53
84%
158%
Commune 7 000 / 15 000 hab
1,71
113%
|
100078
|
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] |
{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
0,53
84%
158%
Commune 7 000 / 15 000 hab
1,71
113%
66%
Communes - 2 500 hab
1,22
85%
70%
Communes 15 000 / 40 000 Hab
1,36
77%
57%
Communes 2 500 / 5 000 hab
1,49
85%
58%
Departements
1,06
70%
66%
HLM
1,11
74%
66%
Marche des entreprises
1,25
147%
117%
Personnes morales de droit Prive
0,79
62%
78%
Regions
0,77
62%
80%
SDIS
1,63
78%
48%
Structures hospitalieres
0,94
73%
78%
Syndicats
1,23
83%
67%
Total général
1,22
79%
64%
….Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 157 -
effet, le comportement d’une collectivité face à son contrat d’assurance est très éloigné de
|
100079
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
celui d’un particulier. Elle ne cherche pas systématiquement à renouveler son contrat
annuellement pour souscrire un contrat moins onéreux. Elle cherche plutôt la stabilité du fait
de procédures parfois lourdes et couteuses. Les tarifs pratiqués sont donc le résultat d’un
ensemble de politiques tarifaires successives, souvent représentatives des évolutions du
marché et qui subissent ensuite des hausses indiciaires voire même des hausses au-delà de
l’indice. Le but de ce contrôle n’est donc pas de vérifier que le tarif GLM est en adéquation
avec la politique tarifaire en vigueur au moment de l’étude mais bien de montrer que le tarif
théorique permet l’équilibre technique du portefeuille. C’est pour cette raison que nous avons
|
10008
|
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{
"title": "2016_3090fc160532a2ee243c3ca4be83d406.pdf"
}
|
l’anticipé.
On rappelle qu’on étudiait une rente , évaluée de manière actuariellement neutre, servie à une
population fictive, au cours de chaque période. On s’intéresse ici à l’établissement de ce compte sur
une année d’exercice comptable , entre le 01/01/T (à l’ouverture) et 31/12/T (à la fermeture). En
particulier, la population est âgée de ans à l’ouverture, où elle est composée de rentiers, et
âgée de ans à la fermeture, où elle est composée de rentiers.
On se situe dans un cadre simplifié, où chaque individu bénéficie du même niveau de rente, versée
annuellement, et où on ne considère pas de frais, ni d’options spécifiques (pas de réversion etc.).
Ainsi à l’ouverture, le solde du compte est le montant réglementaire des provisions mathématiques :
|
100080
|
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
ajouté deux colonnes supplémentaires, mettant en évidence les ratios sinistres sur cotisations
(S/C). Ces ratios nous éclairent sur l’équilibre technique du portefeuille. Sans ces ratios il serait
impossible de juger si la hausse de 22% est justifiée ou non. Globalement, du fait des coûts de
réassurance et de frais d’acquisition et d’administration, la hausse de 22% est tout à fait
logique et correspond à la réalité technique. Il nous faut maintenant regarder les résultats par
type de collectivité. Ceux-ci peuvent paraitre beaucoup plus disparates à première vue. C’est
pourquoi il est important de préciser deux points.
En premier lieu, un fort écart de tarif peut s’expliquer par un ratio sinistre sur cotisations
|
100081
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
dégradé. C’est le cas le plus simple qui concerne par exemple les communes de moins de 2 500
habitants, les départements ou les HLM. L’autre élément qui est à prendre en compte est la
répartition de la mutualisation qui explique des résultats qui peuvent paraître surprenants.
Par exemple, pour le marché des entreprises, la hausse de 25% du tarif ne semble pas
suffisante pour atteindre un certain équilibre. La raison est qu’un unique dossier important a
eu lieu sur cette période et dégrade le résultat. En réalité, ce constat est plutôt rassurant car
il signifie que les répartitions que nous avons effectuées sur les dossiers importants ont permis
de ne pas polluer le GLM et donc de véritablement étaler celles-ci sur l’ensemble du
|
100082
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
portefeuille. La raison est la même lorsque le constat est inverse : pour les conseils régionaux
par exemple, le tarif diminue de 23% ce qui fait passer le S/C de 62% à 80%. Ceci s’explique
parce qu’il y a eu proportionnellement plus de dossiers importants sur cette courte période
que sur l’historique sur lequel ont été calculés les tarifs GLM.Arbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 158 -
Nous pouvons maintenant analyser la distribution des écarts à un niveau plus fin c’est-à-dire
contrat par contrat (figure 75).
Figure 75 : Comparatif ancien et nouveau tarif.
|
100083
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] |
{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
Figure 75 : Comparatif ancien et nouveau tarif.
La distribution est plutôt symétrique et centrée autour de 1. En revanche, elle est relativement
étalée. De nombreux risques présentent des écarts de plus ou moins 40%.
Globalement, le nouveau tarif semble donc valide. Il nous permet d’atteindre l’équilibre. La
validation individuelle du tarif, c’est-à-dire par risque ou collectivité, fait l’objet d’une
campagne de recette réalisée par les métiers.
Il convient maintenant de s’intéresser à la robustesse du nouveau tarif. Autrement dit, dans
quelle mesure les différents paramètres estimés sont sensibles aux différentes hypothèses
retenues.
0
5 000
10 000
15 000
20 000
25 000
30 000
35 000
|
100084
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{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
0
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0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2 2,1 2,2 2,3 2,4 2,5 2,6 2,7 2,8 2,9 3 3,1 3,2 3,3 3,4 3,5 3,6 3,7 3,8 3,9 4
Fréquence
Ratio Théorique / Réel
Ratio Tarif théorique/Tarif réel par contratArbitrage entre mutualisation et segmentation : le cas des assurances dommages de
collectivités. M.PLISSON, B.ROSSARD
- 159 -
ANNEXE 7 : Tests de sensibilité sur différents paramètres
En complément de la validation précédente, nous allons maintenant étudier la sensibilité du
modèle aux différentes hypothèses. Cette partie est très importante car elle permet de vérifier
|
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] |
{
"title": "2017_7ea3881ad2d52a732ed5adbd24860856.pdf"
}
|
que les hypothèses retenues ne remettent pas en cause la pertinence du modèle final.
Sensibilité aux sous périodes
Ce test répond aux fortes évolutions qu’a connues le portefeuille entre 2001 et 2012. L’objectif
est de refaire l’ensemble de la modélisation GLM sur des bases d’apprentissage différentes
(ici 2001-2009 puis 2001-2004 enfin 2005-2009) puis d’appliquer nos trois jeux de résultats
sur la période 2010-2012 pour en mesurer les écarts avec les charges sinistre réelles. Les
résultats sont présentés sur le tableau suivant (figure 76) pour la garantie Incendie.
Figure 76 : Sensibilité aux sous-périodes retenues pour le calibrage du modèle.
Dans l’ensemble des scénarios, nous nous apercevons que le modèle surestime la charge
|
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