Optimisation in Non-Life Insurance

Hanspeter Schmidli

In this course we review two optimisation problems. The first problem is to minimise the ruin probability by proportional reinsurance. The results are complemented by some asymptotic considerations of the minimal ruin probability and the optimal strategy. The second problem is to maximise the expected discounted dividend payout. Both problems are solved via the Hamilton-Jacobi-Bellman approach. We show how the problems can be approached, and what problems may occur.