# Actuarial Study of Non-life Insurance

#### Teacher

Department: Finance

### 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

Part 1. A priori pricing
1.1 Frequency / severity approach: general results on fdr, density, moments, fgm
1.2 Regression for frequency: Poisson, binomial, negative binomial laws and their generalization
1.3.Regression for severity: gamma laws, inverse Gaussian, log normal, Pareto,
1.4 Premium calculation: principles, deductible, limit
1.5.Indemnity / lump-sum approach: Bernoulli, Tweedie Laws
1.6. Exposure approach: Exposure curves, 1-inflat laws, MBBEFD
Part 2 - Subsequent Pricing
1.1 Credibility models: parametric and Buhlman-Straub models
1.2 Comparison of models: Lorenz curve, high-risk index
1.3. Segmentation and mutualization
Part 3 - Non-life provisioning
1.1 Basics and triangles: PSAP
1.2 Deterministic method: chain-ladder, London-chain, London-pivot
1.3 Stochastic methods: 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.