Risk Theory - 3A/MS/M2

Objective

The purpose of this course is to present the basic mathematical concepts of damage insurance. The objective of Risk Theory is to provide theoretical models of the cost and number of claims in order to deduce the associated risk and to price insurance contracts.
At the end of this course, students should be able to : 

• Use the individual and collective model of claims occurrence in non-life insurance.
• Apply the collective model to reinsurance
• Understanding the Poisson process and its application in ruin theory
   

Planning

1. Preliminaries - Reminders, generating functions. 
2. Premium principle and risk measurement.
3. Risk comparison.
4. Insurance models - Individual model, collective model.
5. Theory of ruin - Poisson's process, Lundberg's model, probability of ruin.

References

• Beard R., Pentikainen R., & E. Pesonen (1984), Risk Theory. Chapman and Hall [INSEE].
• Buhlmann H.  (1970), Mathematical Methods in Risk Theory. Springer [36 BUH 00 A].
• Charpentier, A., & M. Denuit (2004), Mathématiques de l'assurance Non-Vie, tome 1: Principes Fondamentaux de la Théorie du Risque. Economica [36 DEN 00 B].
• Daikin, C.D., Pentikainen, T., & M. Pesonen (1994), Practical Risk Theory for Actuaries. Chapmann and Hall [78 DAY 00 A].
• Gerber, H.(1979), An Introduction to Mathematical Risk Theory. Huebner Foundation for insurance [78 GER 00 A].
• Heilmann, W. R. (1988), Fundamentals of Risk Theory, VVW Karlsruhe [36 HEI 00 A].
• Straub, E. (1988), Non Life Insurance Mathematics. Springer [78 STR 00 A].