Optimal dynamic reinsurance policies for large insurance portfolios

Abstract

We consider a large insurance company whose surplus (reserve) is modeled by a Brownian motion. The company invests its surplus in stock market assets which may or may not contain an element of risk. To minimize the insurance risk there is a possibility to reinsure a part or the whole insurance portfolio. We consider the case of proportional reinsurance. There is a transaction cost, which manifests itself in the fact that the safety loading of the reinsurer is larger than that of the cedent. Stochastic optimal control theory is used to determine the optimal reinsurance policy which minimizes the ruin probability of the cedent.