An Intertemporal Preference with Risk and Loss Aversion

Abstract

We study the consumption and portfolio selection problem of an agent who faces consumption irreversibility: there is disutility from changing consumption levels. The derived preference exhibits intertemporal loss aversion toward consumption changes with the previous consumption level being the reference point. The optimization problem involves the non-monotonic and non-concave utility function. By combining a duality method and the super-contact principle, we derive the closed-form solution. We show that the consumption policy involves an inaction interval for the consumption-wealth ratio, which can explain the four stylized facts about consumption at once. The optimal portfolio choice exhibits a U-shape in the inaction interval, which sheds light on the empirical debate on the relationship between a household's financial wealth and the share invested in risky assets.