Robust consumption and portfolio choices with habit formation

Abstract

This paper explores the effect of homothetic model uncertainty on an agent's optimal consumption and portfolio choices with multiplicative habit formation. We solve the max-min expected utility problem to obtain the optimal consumption and portfolio rules. Detection error probabilities, which were calculated using Monte Carlo simulations, calibrate reasonable ambiguity aversion parameters. Results indicate that ambiguity leads to a more aggressive consumption strategy but more conservative investment choices and that the opposite effect is observed on the optimal decision between model uncertainty and habit formation. Notably, we find that the dynamics of investment are a mean-reverting process and that model uncertainty can increase this reversion rate. Furthermore, we discover a distinction between ambiguity and risk. The practical significance of this article is that it provides an alternative theoretical explanation for the excess sensitivity and smoothness puzzles of consumption from the perspective of ambiguity.