The objective of this course is to introduce the basic probabilistic models used in non-life insurance. It first presents the essential characteristics and principles of insurance. It then reviews the probability distributions used to model claim frequency and claim severity, as well as the tests used to identify them. The techniques for calculating insurance premiums and their properties are then detailed. Finally, the course addresses the insurer's solvency problem, first in a static and then in a dynamic framework.
- Enseignant éditeur: Nagot Isabelle
1) Introduction: 1. History of insurance and general principles 2. Utility function and insurance
2) Review of probability and statistics: 1. Distributions 2. Moments, generating function 3. Convolution 4. Extreme value distributions 5. Identification of distributions: QQ-plot, moments, tests 6. Central limit theorem, law of large numbers 7. Gini index 8. Risk pooling
3) Collective model
4) Definition and properties of the insurance premium function 5) Ruin theory
