In this paper, we study an optimal reinsurance strategy combining a proportional and an excess of loss reinsurance. We refer to a collective risk theory model with two classes of dependent risks; particularly, the claim number of the two classes of insurance business have a bivariate Poisson distribution. In this contest, our aim is to maximize the expected utility of the terminal wealth. Using the control technique, we write the Hamilton-Jacobi-Bellman equation and, in the special case of the only excess of loss reinsurance, we obtain the optimal strategy in a closed form, and the corresponding value function.

Optimal Dynamic Proportional and Excess of Loss Reinsurance under Dependent Risks

GOSIO, CRISTINA;LARI, ESTER CESARINA;RAVERA, MARINA
2016

Abstract

In this paper, we study an optimal reinsurance strategy combining a proportional and an excess of loss reinsurance. We refer to a collective risk theory model with two classes of dependent risks; particularly, the claim number of the two classes of insurance business have a bivariate Poisson distribution. In this contest, our aim is to maximize the expected utility of the terminal wealth. Using the control technique, we write the Hamilton-Jacobi-Bellman equation and, in the special case of the only excess of loss reinsurance, we obtain the optimal strategy in a closed form, and the corresponding value function.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/839711
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