Mean-VAR Model with Stochastic Volatility

The objective of this article is the research of optimal portfolio strategy under a probability constraint of type Value-at-Risk in setting of stochastic volatility model. Our decision problem is the optimal combination of risky asset and certain asset by maximizing the utility function under the VaR constraint that is limited by a loss proportional to current return. The empirical results show that the VaR constraint decreases the amount invested in risky asset gradually over time. We also note that volatility has a significant impact on the optimal solution. Furthermore, this approach is more appropriate when the investor sets a confidence level high enough and low holding period. In addition, this model allows us to better understand the form of the distribution and offers the advantage to the investor to take account of asymmetric and leptokurtic distributions of stock market returns.