研究了Heston随机波动率模型下带有负债过程的动态投资组合问题,并且假设风险资产价格过程满足Heston随机波动率模型,负债过程服从带漂移的布朗运动.金融市场由一种无风险资产和一种风险资产所构成.首先,应用动态规划原理得到相应值函数所满足的HJB方程.然后,假设投资者对风险的偏好程度满足双曲绝对风险厌恶(HARA)效用函数,并应用Legendre变换法和分离变量法得到在HARA效用函数下最优投资策略的显示解.最后,给出数值算例分析部分市场参数对最优投资策略的影响.

This paper studies a dynamic portfolio selection problem with liability process under the Heston's stochastic volatility model. The price process of the risky asset is assumed to satisfy the Heston model, and the liability process is supposed to be driven by the drifted Brownian motion. The financial market consists of one risk-free asset and one risky asset. Firstly, we apply dynamic programming principle to achieve the HJB equation for the corresponding value function. Then, the preference degree of investors for risks can be described by HARA utility function, and the explicit solutions to the optimal investment strategies under HARA utility criterion is successfully obtained by using Legendre transformation method and variable separation technique. Finally, a numerical example is given to illustrate the effect of some market parameters on the optimal investment strategy.