Optimal reinsurance: minimize the expected time to reach a goal

Abstract

In this paper, we consider an optimal reinsurance problem. The surplus model of the insurance company is approximated by a diffusion model with the drift coefficient . The insurance company employs reinsurance to reduce the risk. is the proportion of each claim paid by the company and the remainder proportion of the claim is paid by the reinsurer. is the rate at which the premiums are diverted to the reinsurer, thus it holds in general. We discuss two cases: (i) non-cheap reinsurance (when ), (ii) cheap reinsurance (when ). The objective of the insurance company is to make an optimal decision on reinsurance to reach a goal (a given surplus level) in minimal expected time. We disclose that for some case it is not suitable to search optimal decisions by minimizing the expected time to reach a goal. In order to deal with this case, we study two other methodologies (ruin probability minimization and expected discount factor maximization) for the optimal strategy selection problem in reinsurance decision.