Abstract: This paper considers an optimal  portfolio choice problem under Stein-Stein stochastic volatility model and dynamic VaR constraint. The investor aims to maximize the expected power utility of the terminal wealth, and the financial  market consists of one risk-free asset and one risky asset whose price process is described by   Stein-Stein stochastic volatility model. At the same time, the investor hopes to limit the potential   risk over investment horizon by a dynamic VaR constraint. Adopting the stochastic dynamic programming    approach and Lagrange multiple method, we derive the closed-form expressions of the optimal strategy    as well as the optimal value function in a special case. Moreover, economic implications and numerical    analysis are proposed to illustrate the impacts of stochastic volatility and dynamic VaR constraint    on the investor's optimal strategy.

Key words: dynamic VaR constraint , stochastic volatility, optimal portfolio strategy, dynamic programming, utility maximization