Two Types Of Risk Models Optimal Investment And Reinsurance Strategies

In insurance practice, the insurance company can divert and diverge the risks by purchasing reinsurance. At the same time, the insurance company can also invest some of the surplus in the financial market to increase wealth. Apparently, risky investment can be dangerous and reinsurance will diverge part of the premiums to the reinsurance company. Therefore, it is of important practical significance for the insurance company to study the optimal investment and optimal reinsurance policy. Further more, with the development of insurance theory and practice, dividends are also taken into account in the research of risk theory.In this thesis, we study two optimization problems on investment and reinsurance.In chapter 3, we study the optimal investment strategy and the optimal reinsurance policy in the sense of maximizing the total dividends, where the surplus associated to the underlying investment and reinsurance policy satisfies an Ito stochastic differential equation and the dividend distribution follows the threshold rule. By applying the stochastic dynamic programming method, an HJB equation related to the problem is obtained, and the optimal investment strategy and the optimal reinsurance policy thus follows by solving this HJB equation. In addition, the impacts of investment and reinsurance on dividend are also illustrated by numerical calculation.In chapter 4, we study the jump- diffusion risk model with investment and XL reinsurance. The optimal investment strategy and the optimal reinsurance policy such that the ruin probability attains its minimum are obtained, and the relations between the ruin probability and some of the parameters characterizing investment and reinsurance are also shown by numerical calculation.