Actuarial Study of Non-life Insurance
Teacher
BARADEL Nicolas
Department: Finance
ECTS:
4
Course Hours:
24
Tutorials Hours:
0
Language:
French
Examination Modality:
written exam
Objective
This course introduces the main models in non-life insurance. Emphasis will be placed on classical econometric models (GLM) but alternative techniques will also be presented. The three main families of models ({0,1}, counting and positive variable) will be presented, with illustrative examples in each case in non-life insurance. Finally, the problem of reserving will be addressed, and the main models will be detailed. Throughout the course, R codes will be presented and applied to insurance data.
At the end of the course, the student will know how to
- understand the main pricing and provisioning models
- know how to use computer tools to build a pricing and calculate non-life insurance reserves
Planning
Partie 1. Tarification a priori
1.1 Approche fréquence / sévérité : résultats généraux sur fdr, densité, moments, fgm
1.2 Régression pour la fréquence : Lois de Poisson, binomiale, binomiale négative et leur généralisation
1.3 Régression pour la sévérité : lois gamma, gaussienne inverse, log normale, Pareto,
1.4 Calcul de la prime : principes, franchise, limite
1.5 Indemnisation / approche forfaitaire : Lois de Bernoulli et de Tweedie
1.6. Approche de l'exposition : Courbes d'exposition, lois 1-inflat, MBBEFD
Partie 2 - Tarification a posteriori
1.1 Modèles de crédibilité : modèles paramétriques et modèles de Buhlman-Straub
1.2 Comparaison des modèles : Courbe de Lorenz, indice de risque élevé
1.3. Segmentation et mutualisation
Partie 3 - Provisionnement non-vie
1.1 Bases et triangles : PSAP
1.2 Méthode déterministe : Chain-Ladder, London-Chain, London-Pivot
1.3 Méthodes stochastiques : Mack, bootstrap, GLM
References
Charpentier, A. (2014). Computational Actuarial Science, with R. CRC Press.
Denuit, M. & Charpentier, A. (2004). Mathématiques de l'assurance non-vie, tome 1: principes fondamentaux de théorie du risque. Economica. [36 DEN 00 A]
Denuit, M. & Charpentier, A. (2005). Mathématiques de l'assurance non-vie, tome 2: tarification et provisionnement. Economica [36 DEN 00 B]
de Jong, P. & Heller, G.Z. (2008). Generalized linear models for insurance data. Cambridge University Press.
Ohlsson, E. & Johansson, B. (2010) Non-life insurance pricing with generalized liner models. Springer.
Wüthrich, M. & Merz, M. (2008) Stochastic Claims Reserving Methods in Insurance. Wiley.