A preference change and discretionary stopping in a consumption and porfolio selection problem

Abstract

We study an optimal consumption-portfolio selection problem in which an economic agent is able to choose a discretionary stopping time in a continuous-time framework. We focus on studying the problem for the case where the agent’s preference changes around the stopping time. We obtain the optimal policy in an explicit form by solving free boundary value problems. If the agent’s coefficient of relative risk aversion becomes higher (lower) after the stopping time, then the optimal policy is to stop as soon as the wealth level touches down (up) to the critical wealth level.