关键词: 最优投资组合, Heston随机波动率, 动态VaR约束, 动态规划

Abstract: This paper considers an optimal portfolio choice problem under Heston stochastic volatility model and a dynamic VaR constraint. Assume the financial market consists of one risky asset, like stock, whose price satisfies a Heston stochastic volatility model and one risk-free asset, like bond. The investor aims to maximize the expected power utility of the terminal wealth. At the same time, the investor hopes to manage the portfolio risk by a dynamic VaR constraint, which means she will compute the VaR of her portfolio continually. Using the stochastic dynamic programming approach, we solve the problem numerically. Finally, economic implications are proposed to illustrate the impacts of Heston stochastic volatility and dynamic VaR constraint on the investor’s optimal strategy. Our numerical experiment shows that the dynamic VaR criterion is an effective tool to manage the risk during the whole investment period.

Key words: portfolio optimization, Heston stochastic volatility, dynamic VaR constraint, dynamic programming approach.