Geodesic
Reinsurance optimal strategy of a loss excess
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2011), pp. 17-22 
A. N. Gromov. Reinsurance optimal strategy of a loss excess. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2011), pp. 17-22. http://geodesic.mathdoc.fr/item/VMUMM_2011_4_a2/
@article{VMUMM_2011_4_a2,
     author = {A. N. Gromov},
     title = {Reinsurance optimal strategy of a loss excess},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {17--22},
     year = {2011},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2011_4_a2/}
}
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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.