LIFETIME CONSUMPTION AND INVESTMENT FOR WORST-CASE CRASH SCENARIOS

Abstract

We investigate worst-case optimal consumption and portfolio decisions under the threat of a market crash on an infinite time horizon. We provide a closed-form solution for constant relative risk aversion and establish a rigorous verification result. More specifically, using martingale arguments we demonstrate that the optimal consumption-portfolio strategy can be characterized as the indifference strategy that achieves the best performance in the no-crash scenario. In addition, we find a dual characterization of the optimal strategy as the indifference strategy that minimizes the crash exposure. Finally, we quantify the impact of the crash on consumption and portfolio choice and analyze it in terms of the investor's risk and time preferences and prudence.