Jump - Diffusion Risk Model Of Optimal Investment And Reinsurance Strategy

In recent years, due to severe competition in the insurance industry, the insurance company get a lot of benefits to improve their solvency from the investment of the money at its disposal. At the same time, in order to reduce the risk of large claims, the insurance company takes reinsurance policy for claims. Apparently, risky investment can be dangerous, and reinsurance needs to given part of the premium to the reinsurnance company. Therefore, subject to the control of both investment and reinsurance policies, minimizing the probability of ruin or maximizing the expected wealth utility of the reinsurance company has become important problems which each insurance company has to face, and it has a very important theoretical and practical significance.In this paper, the surplus process of the insurance company is assumed to follow the the jump-diffusion risk process. In addition, the insurance company is allwed to invest in a risk-free asset and risky assets and to purchase proportional reinsurance. By the dynamic programming method of the stochastic optimal control theory, the Hamilton-Jacobi-Bellman(HJB) equation of the maximal expected utility function is obtaned. Explicited expressions for the maximal expected exponential utility and the corresponding optimal policies are obtained. We also investigate the effects of the parameter on the optimal strategies by numerical calculation.The risky asset models involving in this paper are the following: multiple risk assets satisfying the geometric Brownian motion, the constant elasticity of variance (CEV) model and the Heston random variance model. After the second chapter we study the different risk model, and obtain the corresponding conclusions, and also get the numerical calculation and economic analysis.