Portfolio selection with consumption ratcheting

Abstract

In this paper we study the portfolio selection problem of a finite-lived agent who does not tolerate a decline in standard of living. The preference can be regarded as exhibiting extreme-form of habit formation and also related to loss aversion in the prospect theory. We show that the agent's optimal portfolio exhibits a trend chasing behavior and the portfolio share of the risky asset fluctuates between 0 and the value of an unconstrained individual; the fluctuations do not attenuate as time gets near the end of the planning horizon. We also explore implications of the model for asset pricing and show that the model has a potential to match better the recent US data than traditional habit models. We provide a complete solution to the problem by considering a transformed problem, which is similar in its formal structure to an irreversible incremental investment problem and equivalent to an infinite series of optimal stopping problems. (C) 2018 Elsevier B.V. All rights reserved.