Stochastic reinsurance models and their optimization

Discrete-time models of insurance company performance are considered. It is supposed that in order to satisfy timely the policyholders claims the company can use additional capital injections. Either personal funds of shareholders or bank loans serve the source of such injections. It is also assumed that insurer can use reinsurance treaties to reduce the ruin probability. The aim of the thesis is to establish the reinsurance strategies minimizing the expected discounted capital injections. The optimal strategies are determined for one-step and multi-step processes. The sensitivity of optimal strategy to fluctuations of the model parameters is studied. The model stability with respect to small perturbations of claim distribution is proved. The limit behavior of the insurer’s surplus under the optimal reinsurance strategy is also investigated.