Asymptotic Analysis of Insurance Models with Bank Loans and Reinsurance

Discrete-time models became popular in actuarial mathematics during the last two decades, since in many cases they reflect more precisely the real situation. In order to control the insurance process a company may use such tools as reinsurance, bank loans, investment and dividends. Below we consider an insurance model with bank loans and non-proportional reinsurance. First, we establish the optimal policy of bank loans in the framework of cost approach. Second, the limit behavior of the company surplus under optimal control is investigated. In particular, the strong law of large numbers (SLLN) and central limit theorem (CLT) are proved. The model stability with respect to small perturbations of the underlying distributions is also treated.