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Optimal risk control and dividend policies under excess of loss reinsurance. (English) Zbl 1076.93046

Summary: We study the optimal reinsurance policy and dividend distribution of an insurance company under excess of loss reinsurance. The objective of the insurer is to maximize the expected discounted dividends. We suppose that in the absence of dividend distribution, the reserve process of the insurance company follows a compound Poisson process. We first prove existence and uniqueness results for this optimization problem by using singular stochastic control methods and the theory of viscosity solutions. We then compute the optimal strategy of reinsurance, the optimal dividend strategy and the value function by solving the associated integro-differential Hamilton-Jacobi-Bellman variational inequality numerically.

MSC:

93E20 Optimal stochastic control
49L20 Dynamic programming in optimal control and differential games
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
65N06 Finite difference methods for boundary value problems involving PDEs
91B30 Risk theory, insurance (MSC2010)
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