MULTI-ASSET PORTFOLIO OPTIMIZATION WITH STOCHASTIC SHARPE RATIO UNDER DRAWDOWN CONSTRAINT

We consider an investor who seeks to maximize his expected utility of the portfolio, consisting of multiple risky assets and one risk-free asset, derived from the terminal wealth relative to the maximum wealth achieved over a fixed time horizon. This is achieved under a portfolio draw down constraint, in a market with local stochastic volatility. In empirical application, considering two risky assets, the assets have been identified with the help of pairs trading. In the absence of closed form solution of the value function and the optimal strategy, we obtain the approximates of these quantities using coefficient series expansion techniques and finite difference schemes. We utilize the risk tolerance factor function to ease our approximations of this value functions and the strategies. All the parameters were estimated from the triplets and used to illustrate and compare the stochastic volatility with the constant volatility situation, and how an investor can deploy different portfolio plans.