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Optimal proportional reinsurance policies in a dynamic setting. (English) Zbl 0971.91039
A dynamic proportional reinsurance strategy \(b_t\) is considered, where \(b_t\) is the proportion of the portfolio which the company is willing to keep at time \(t\). (So \(1-b_t\) is the reinsured part of the portfolio). The aim in choosing \(b_t\) is to minimize the ruin probability. It is shown that for the diffusion model the optimal \(b_t\) is constant. Under the Cramér-Lundberg model a functional equation (containing integrals, derivatives and infimum) is derived which connects the optimal strategy and the survival probability. Examples of numerical solution are presented for exponentially and Pareto distributed claim sizes.

MSC:
91B30 Risk theory, insurance (MSC2010)
93E20 Optimal stochastic control
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