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An optimal reinsurance problem in the Cramér-Lundberg model. (English) Zbl 1377.93174
Summary: In this article, we consider the surplus process of an insurance company within the Cramér-Lundberg framework with the intention of controlling its performance by means of dynamic reinsurance. Our aim is to find a general dynamic reinsurance strategy that maximizes the expected discounted surplus level integrated over time. Using analytical methods we identify the value function as a particular solution to the associated Hamilton-Jacobi-Bellman equation. This approach leads to an implementable numerical method for approximating the value function and optimal reinsurance strategy. Furthermore we give some examples illustrating the applicability of this method for proportional and XL-reinsurance treaties.

##### MSC:
 93E20 Optimal stochastic control 91B30 Risk theory, insurance (MSC2010) 93A30 Mathematical modelling of systems (MSC2010) 60G99 Stochastic processes
##### Keywords:
Cramér-Lundberg model; reinsurance; stochastic control
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