In this paper, we study an optimal investment and reinsurance problem in which the interest rate is driven by the Vasicek process and two dependent classes of insurance business are correlated through a common shock component. The goal of insurer is to find an optimal investment-reinsurance strategy to minimize the variance of terminal net wealth for a given expected terminal net wealth. By using the linear-quadratic optimal control theory and the corresponding Hamilton-Jacobi-Bellman (HJB) equation, the closed-form expressions for the value function and optimal strategies are obtained under the special case of perfect correlation between the bond and stock processes. We present that the solution of the HJB equation is no longer a classical solution, but a viscosity solution due to the non-negativity constraint of the reinsurance strategy. Furthermore, the efficient strategies and efficient frontier are derived explicitly. Finally, we explore some numerical examples to show the influence of model parameters on the optimal investment and reinsurance strategies.

在本文中，我们研究了一个最优投资和再保险问题，其中利率由 Vasicek 过程驱动，两个依赖类别的保险业务通过一个共同的冲击分量相关联。保险公司的目标是找到一个最优的投资-再保险策略，以最小化给定预期终端净财富的终端净财富方差。利用线性二次最优控制理论和相应的Hamilton-Jacobi-Bellman(HJB)方程，得到了债券和股票过程完全相关的特殊情况下价值函数和最优策略的闭式表达式。我们提出，由于再保险策略的非负性约束，HJB方程的解不再是经典解，而是粘性解。此外，有效策略和有效边界被明确推导出来。最后，我们探索了一些数值例子来展示模型参数对最优投资和再保险策略的影响。