Abstract
In this paper, we consider optimal proportional reinsurance from an insurer's point of view to maximize the adjustment coefficient. We obtain the explicit expressions for the optimal results in the diffusion approximation case as well as in the jump-diffusion case. Further, we derive a sharper bound on the ruin probability. When the claim sizes are exponentially distributed, we can prove that the Lundberg's inequality also holds for the ruin probability in the diffusion approximation case. Some numerical examples are presented to show that the ruin probability in the diffusion approximation case sometimes underestimates the ruin probability.
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