随机波动率市场存在股票误价时的最优投资策略

摘要

本文研究了随机波动率市场中存在股票误价(mispricing)时的最优投资组合选择问题.假设投资者的目标是最大化终端财富的期望幂效用;其可投资于无风险资产、市场指数和两支相同权益或近似度极高的股票,其中至少有一支股票存在误价；市场收益的波动率和股票系统风险由Heston随机波动率模型刻画.运用动态规划方法和Lagrange乘子法,分别得到不存在/存在有限卖空约束时,投资者的最优投资策略及最优值函数的解析式,并通过理论分析和数值算例,阐述了投资时间水平和价格随机误差对最优投资策略的影响.%This paper investigates an optimal portfolio selection problem in a market with mispricing and stochastic volatility.The investor's objective is to maximize the expected power utility of the terminal wealth,and the financial market consists of one risk-free asset,one risky asset representing the market index,and a pair of stocks whose prices are mispriced.Meanwhile,the volatilities of the market index and system risk are described by Heston stochastic volatility model.Without/with limited short selling constraints,the closed-form expressions of the optimal strategies and the optimal value functions are derived by the dynamic programming approach and the Lagrange multiple method.Moreover,economic implications and numerical examples are provided to illustrate that how the investment horizon and mispricing error affect the optimal strategies.