Robustness of the reinsurance policy: minimizing the probability of ruin

Abstract

In this paper, we consider the optimal reinsurance problem for an insurer who worries about the existence of the ambiguity with the objective of minimizing the probability of ruin. We assume that the surplus of the insurer is described by a diffusion process. By the dynamic programming principle, we obtain the HJB equation of the value function and give the closed form of the robust reinsurance policy and value function. We can see that the robust reinsurance policy is same as the optimal reinsurance policy in Schmidli (2001), while the value functions are different.