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. 72, N 2, 2017. P. 0].

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.