中文摘要：

本文将Merton的投资模型拓展到随机市场系数模型。在典型投资问题对戍的动态规划中，值函数一般用Bellman方程的粘性解表示。本文通过指数变换把偏微分方程转变成一个半线性的抛物线方程，证明了其值函数连续解的存在性，并在此基础上给出了企业的最优投资组合策略。

英文摘要：

The Merton investment model is extended to the case with stochastic volatility. In the dynamic program corresponding to typical investment problems, the value function is generally represented by the viscosity solution of the stochastic partial differential equation. In this paper, the partial differential equation is transferred to a semi-linear parabolic equation by using the exponential transformation, the existence of the continuous solution of the value function is proven. Furthermore, the optimal investment policy is obtained.