Optimal Reinsurance and Investment Problem with Stochastic Interest Rate and Stochastic Volatility in the Mean-variance Framework

This paper studied an optimal reinsurance and investment problem for insurers under the mean-variance criterion in the stochastic interest rate and stochastic volatility environment, where the financial market consists of two assets: one is the risk-free asset (i.e bond) and the other is the risky-asset (i.e stock) whose volatility satisfying the Heston model. Assume that the interest rate is driven by Vasicek interest rate model and the surplus process is approximated by diffusion approximation model. In order to hedge the risk of the insurance, proportional reinsurance is considered. And the insurer wishes to look for the optimal reinsurance and investment strategies to minimize the variance of the terminal wealth for a given expected terminal wealth. By employing dynamic programming principle and Lagrange duality theorem, the optimal reinsurance and investment strategies and the efficient frontier are explicitly obtained. Finally, some special cases and sensitivity analysis are provided to illustrate our results. Key–Words: Optimal reinsurance and investment strategy; Vasicek interest rate; Stochastic volatility; meanvariance framework; the efficient frontier;