Optimal Retirement in a General Market Environment

Abstract

We study an optimal retirement, consumption/portfolio selection problem of an economic agent in a non-Markovian environment. We show that under a suitable condition the optimal retirement decision is to retire when the individual’s wealth reaches a threshold level. We express the value and the optimal strategy by using the strong solution of the backward stochastic partial differential variational inequality (BSPDVI) associated with the dual problem. We derive properties of the value function and the optimal strategy by analyzing the strong solution and the free boundary of the BSPDVI. We also make a methodological contribution by proposing an approach to investigate properties of the strong solution and the stochastic free boundary of BSPDVI by combining a probabilistic method and the theory of backward stochastic partial differential equations (BSPDEs).