Robust Portfolio Choice with Derivatives Trading Under Stochastic Volatility

The problem of optimal portfolio choice is solved, in closed form, for an ambiguity averse investor who has access to stock and derivatives markets. The investor can have different levels of uncertainty about models for stock return and its stochastic volatility. Although both types of ambiguity considerably impact the optimal portfolio, we show that stock return ambiguity is more significant for stock allocation whereas volatility uncertainty has larger influence on derivatives trading. As expected, investors with no access to derivatives would not have additional losses from ignoring volatility uncertainty. Access to derivatives market substantially improves portfolio performance and increases welfare loss from neglecting either type of ambiguity. Interestingly, the loss from ignoring ambiguity could be as much as the loss from not trading the derivatives