Reinsurance optimal strategy of a loss excess

Dynamic programming technique is applied to find the optimal strategy for the dynamic XL reinsurance. We consider a risk process modelled 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 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.