The goal of this course is to provide concepts and techniques to model and monitor the risk associated with an insurance portfolio.
Probability and Statistics
An insurance portfolio typically consists of a large number of risks that are identically distributed. For the insurer, it is of utmost importance to have accurate tools to measure the aggregate insurance risk. We will consider several techniques to model claim frequencies in combination with claim sizes to compute or approximate these measures. Valuable concepts in this context are the Capital at Risk (CaR) and the probability of ruin. Clearly, the insurer can affect the aggregate risk through reinsurance. We will consider several reinsurance strategies. Combining claim frequencies and claim sizes is then used to determine a risk-based price for insurance contracts (tariffication). The insurer will invest the premia from the policy holders. This can give rise to credit risk and we introduce the Basel III/IV framework to measure the aggregated credit risk. The insurer can also affect the aggregate insurance risk through premium setting. Particular attention will be devoted to credibility theory and IBNR techniques. Finally, we will consider the theory of extreme risks with emphasis on heavy tailed distributions; also tail dependence will be studied in this framework.
Type of instructions
2 hours lecture a week; 2 hours tutorial biweekly
Type of exams
written exam (90%); assignment (10%).
there is a resit for the exam (90%); the assignment (10%) has no resit.
1. Wuthrich, Mario V., Non-Life Insurance: Mathematics & Statistics (January 7, 2020). (Parts of) Chapters 1 through 4 and 7-9. Available at SSRN: https://ssrn.com/abstract=2319328
2. Slides 'Analysis of Extremes'.