Optimal Investment And Reinsurancestrategies Under The Constant Elasticity Of Variance Model

The insurance company wants to survive in the competitive environment, on the one hand it must do its best to occupy the market, enlarge the profit, increase the capital utilization rate, on the other hand it must try to control insurance risks to maintain stable operation. Therefore, how to choose the best investment and reinsurance strategies, in order to make the insurance company develop well, becomes a very important issue to insurance companies and scholars. In this paper, the optimal investment and reinsurance strategies of the insurance company is studied as the main research basing on the constant elasticity of variance model of the risk assets, and the main work is done as follows:Firstly, this paper studied the optimal investment and proportional reinsurance strategies under the constant elasticity of variance model. The surplus process of the insurance company met the jump diffusion stochastic process, the risk capital market met the constant elasticity of variance(CEV) model. In the process of proportional reinsurance, this paper considered the correlation of underwriting process and the risk capital. The final goal of the insurance company is maximizing the expected utility of wealth. Under this goal, this paper built a model and established the HJB equation according to the stochastic control theory. Then this paper got the analytical expression of the optimal investment reinsurance strategies and the optimal value function. In the end, the influence of various parameters on the optimal strategies is explained.Secondly, this paper studied the optimal investment and mixed reinsurance strategies under the constant elasticity of variance model. This paper assumed that the insurance surplus process meets jump diffusion stochastic process and the venture capital market follows the constant elasticity of variance model. The process of reinsurance is a mixture of proportion reinsurance and excess of loss reinsurance. To the insurance company, the final goal is maximizing the expected utility of wealth. Then this paper established the model, solved the HJB equation and got the analytical expressions of the optimal investment and reinsurance strategies and the optimal value function. By analyzing the instance, the influence of various parameters on the optimal strategy is explained. This paper found that the optimal combined reinsurance strategy is a pure excess of loss reinsurance strategy.Finally, this paper took the benefit of the reinsurance companies into consideration when studying the optimal investment and reinsurance strategies under the constant elasticity of variance model. Aiming at the maximization of the expected utility of the insurance company and the reinsurance company under the CEV model this paper solved the optimal investment and proportional reinsurance strategies of the insurance company.