Uncertainty aversion, robust control and asset holdings

Optimal portfolio rules are derived under uncertainty aversion by formulating the portfolio choice problem as a robust control problem. The robust portfolio rule indicates that the total holdings of risky assets as a proportion of the investor's wealth could increase as compared to the holdings under the Merton rule, which is the standard risk aversion case. With two risky assets an increase in the holdings of the one risky asset is accompanied by a reduction in the holdings of the other asset. Furthermore, in the optimal robust portfolio the investor may increase the holdings of the asset for which there is or less ambiguity, and reduce the holding of the asset for which there is more ambiguity, a result that might provide an explanation of the home bias puzzle.