Reinsurance Optimal Strategy of a Loss Excess / Gromov A.N. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2011. ? 4. P. 17-22 [Moscow Univ. Math. Bulletin. Vol. 66, N 4, 2011.].

Dynamic programming technique is applied to find the optimal strategy for the dynamic XL reinsurance. We consider a risk process modeled by a compound Poisson process and the excess of loss reinsurance determined by the retention level and layer. We find the optimal survival probability as a solution to the corresponding HJB equation and show the existence of the optimal reinsurance strategy. Numerical examples in the case of exponentially, log-normally, and Pareto distributed claims are presented.

Key words: reinsurance, dynamic programming, Hamilton-Jacobi-Bellman equation, measurable selection theorem.