Heston随机波动率模型下的资产负债管理问题

摘要

应用随机最优控制方法研究 Heston随机波动率模型下带有负债过程的动态投资组合问题，其中假设股票价格服从 Heston随机波动率模型，负债过程由带漂移的布朗运动所驱动。金融市场由一种无风险资产和一种风险资产组成。应用随机动态规划原理和变量替换法得出了上述问题在幂效用和指数效用函数下最优投资策略的显示解，并给出数值算例分别分析了市场参数在幂效用和指数效用函数下对最优投资策略的影响。%The stochastic optimal control theory was used to study a dynamic portfolio selection problem with liability process under the Heston's stochastic volatility model.Stock price was assumed to be governed by the Hestonmodel,and the li-ability process was supposed to be driven by the drifted Brownian motion.The financial market consists of one risk-free asset and one risky asset.The explicit solutions to the optimal investment strategies under power utility and exponential utility were obtained by using stochastic dynamic programming principle and variable separation method.Finally,a numerical example was given to illustrate the effect of market parameters on the optimal investment strategy.