Optimal Retirement and Portfolio Selection with Consumption Ratcheting

43 Pages Posted: 29 Oct 2019

See all articles by Junkee Jeon

Junkee Jeon

Kyung Hee University - Department of Applied Mathematics

Kyunghyun Park

Department of Mathematical Sciences, Seoul National University

Date Written: October 13, 2019

Abstract

The purpose of this paper is to study the optimal retirement and consumption/investment decisions of an infinitely lived agent who does not tolerate any decline in her consumption throughout her lifetime. The agent receives labor income but suffers disutility from working until retirement. The agent’s optimization problem combines features of both singular control and optimal stopping. We use the martingale method and study the dual problem, which can be decoupled into a singular control problem and an optimal stopping problem. We provide a closed-form solution of the optimal strategies for the time-separable von-Neumann-Morgenstern utility function. We show that the coefficient of relative risk aversion implied by the optimal portfolio (i.e., the implied coefficient of relative risk aversion, ICRRA) is a constant value smaller than 1. Moreover, we show that the ICRRA is independent of the agent's felicity utility function and depends only on the subjective discount rate and market parameters.

Keywords: Portfolio selection, Consumption ratcheting, Early retirement option, Singular control problem, Optimal stopping problem

JEL Classification: E21, G11

Suggested Citation

Jeon, Junkee and Park, Kyunghyun, Optimal Retirement and Portfolio Selection with Consumption Ratcheting (October 13, 2019). Available at SSRN: https://ssrn.com/abstract=3469081

Junkee Jeon (Contact Author)

Kyung Hee University - Department of Applied Mathematics ( email )

1732 Deogyeong-daero, Giheung-gu,
Yongin, 130-701
Korea, Republic of (South Korea)

Kyunghyun Park

Department of Mathematical Sciences, Seoul National University ( email )

GwanakRo 1, Gwanak-Gu Seoul, 151-747, Republic of
Seoul, 151-747
Korea, Republic of (South Korea)

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