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Optimal dynamic XL reinsurance. (English) Zbl 1059.93135
Summary: We consider a risk process modelled as a compound Poisson process. We find the optimal dynamic unlimited excess of loss reinsurance strategy to minimize infinite time ruin probability, and prove the existence of a smooth solution of the corresponding Hamilton-Jacobi-Bellman equation as well as a verification theorem. Numerical examples with exponential, shifted exponential, and Pareto claims are given.

MSC:
93E20 Optimal stochastic control
91B30 Risk theory, insurance (MSC2010)
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References:
[1] (2003)
[2] Optimal Proportional Reinsurance Policies in a Dynamic Setting pp 16– (2000)
[3] Insurance: Mathematics and Economics 22 pp 75– (1998)
[4] Aspects of Risk Theory (1991) · Zbl 0717.62100
[5] DOI: 10.1016/S0167-6687(00)00049-4 · Zbl 1007.91025 · doi:10.1016/S0167-6687(00)00049-4
[6] Insurance: Mathematics and Economics 26 pp 185– (2000)
[7] Wiley Series in Probability and Statistics 15 (1998)
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