Uncertainty Aversion Robust Control and Asset Holdings

In this paper we formulate the portfolio choice problem as a robust control problem. Extending our previous work [32] , by considering a stochastic investment opportunity set, we derive optimal portfolio rules under uncertainty aversion, in the cases of one and two risky assets. In particular, with two risky assets and one risk-free asset, with the same level of ambiguity aversion for the two assets, we show that the robust portfolio rule could lead to an increase in the total holdings of risky assets as compared to the holdings under the Merton rule, which is the standard risk aversion case. Furthermore the investor is more likely to increase the holdings of the asset for which there is no ambiguity, and reduce the holdings of the asset for which there is ambiguity, a result that might provide an explanation for the home bias puzzle