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Optimal non-proportional reinsurance control. (English) Zbl 1231.91199
Summary: This paper deals with the problem of ruin probability minimization under various investment control and reinsurance schemes. We first look at the minimization of ruin probabilities in the models in which the surplus process is a continuous diffusion process in which we employ stochastic control to find the optimal policies for reinsurance and investment. We then focus on the case in which the surplus process is modeled via a classical Lundberg process, i.e. the claims process is compound Poisson. There, the optimal reinsurance policy is derived from the Hamilton-Jacobi-Bellman equation.

MSC:
91B30 Risk theory, insurance (MSC2010)
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
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