| How invest and purchase reinsurance effectively to maximize the value of the company and minimum risk has become an important topic. In order to find the optimal strategy with practical value, this article mainly studied the optimal investment and reinsurance strategy under the stochastic interest rate and stochastic volatility from two aspects. On the one hand, the insurer’s object is to maximize the power utility function of terminal wealth; On the other hand, the insurer wish to look for an optimal strategy to minimize the variance of the terminal wealth for a given expected terminal wealth. The main research work is as follows.1. The optimization problem based on the rule of power utility and the random environment.By buying a proportional reinsurance, the insurance company spread the risk, and invested in risk-free assets and risky assets, where the interest rate of the risk-free asset is described by the Vasicek interest model and the volatility of the risky asset is given by the Heston model. The insurer wants to make the largest power utility function of terminal wealth, and obtains the corresponding function. Main-ly by using the stochastic dynamic programming algorithm, the HJB equation is obtained. Finally, the optimal reinsurance and investment strategy are obtained.2. The optimization problem based on the mean-variance criterion and the random environment.The insurance company also buy proportional reinsurance and invest the risk-free asset and risky asset, but the target is minimum variance under a fixed value of terminal wealth. For this problem, by employing the Lagrange dual method, the mean-variance problem is changed into the optimal control problem without constraints. In addition, we solve this problem by applying the stochastic dynamic programming method, and the optimal investment and reinsurance strategies of the original problem are obtained by transforming.Finally, some conclusions of the paper and the direction of the future research are given. |
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