Portfolio Management with Stochastic Interest Rates and Inflation Ambiguity

We solve a stock-bond-cash portfolio choice problem for a risk- and ambiguity-averse investor in a setting where the inflation rate and interest rates are stochastic. The expected inflation rate is unobservable, but the investor may learn about it from realized inflation and observed stock and bond prices. The investor is aware that his model for the observed inflation is potentially misspecified, and he seeks an investment strategy that maximizes his expected utility from real terminal wealth and is also robust to inflation model misspecification. We solve the corresponding robust Hamilton-Jacobi-Bellman equation in closed form and derive and illustrate a number of interesting properties of the solution. For example, ambiguity aversion affects the optimal portfolio through the correlation of price level with the stock index, a bond, and the expected inflation rate. Furthermore, unlike other settings with model ambiguity, the optimal portfolio weights are not always decreasing in the degree of ambiguity aversion.