Discrete-Time Insurance Models. Optimization of Their Performance by Reinsurance and Bank Loans

摘要

The popularity of discrete-time models in applied probability is explained as follows. They are more precise in some situations. In other cases they can be used as approximation of the corresponding continuous-time models. So, we consider two discrete-time insurance models and study the quality of their performance. The company reliability or the expected discounted costs incurred by its control can be chosen as an objective function (target or risk measure). It is possible to consider a finite or infinite planning horizon. The control includes reinsurance treaties and/or bank loans. The optimal control (maximizing the reliability or minimizing the costs) is established for the finite planning horizon. Its asymptotic behavior, as the horizon tends to infinity, is also investigated.