An Investor's Optimal Portfolio with Rare Events and Model Uncertainty under Inflation

This paper is concerned with the optimal portfolio choice of an investor under the inflation and rare events impact, where the investor is aversive not only to the risk of loss but also to model uncertainty. An investor allocates his assets to the risky asset and the riskless asset. First, we obtain the dynamics of consumer-basket-price with inflation by using formula. Second, under maximizing the expected utility of intermediate consumption and terminal wealth discounted by inflation, the value function of ambiguity aversion investors is characterized. Through the dynamic programming principle, we derive the HJB equation satisfied by the value function of an investor's optimal consumption and portfolio. Third, applying market decomposition method to solving the HJB equation, the optimal consumption and portfolio policy for investors is obtained. Finally, the effect of the ambiguity aversion, risk aversion and inflation on an investor's optimal allocation strategy is analyzed by numerical simulation.