Market crashes, correlated illiquidity, and portfolio choice

The recent financial crisis highlights the importance of market crashes and the subsequent market illiquidity for optimal portfolio selection. We propose a tractable and flexible portfolio choice model where market crashes can trigger switching into another regime with a different investment opportunity set. We characterize the optimal trading strategy in terms of coupled integro-differential equations and develop a quite general iterative numerical solution procedure. We conduct an extensive analysis of the optimal trading strategy. In contrast to standard portfolio choice models, changes in the investment opportunity set in one regime can affect the optimal trading strategy in another regime even in the absence of transaction costs. In addition, an increase in the expected jump size can increase stock investment even when the expected return remains the same and the volatility increases. Moreover, we show that misestimating the correlation between market crashes and market illiquidity can be costly to investors.