Optimal Retirement Under Partial Information

44 Pages Posted: 19 Oct 2020 Last revised: 8 Jun 2021

See all articles by Kexin Chen

Kexin Chen

The Chinese University of Hong Kong (CUHK) - Department of Statistics

Junkee Jeon

Kyung Hee University - Department of Applied Mathematics

Hoi Ying Wong

The Chinese University of Hong Kong (CUHK) - Department of Statistics

Date Written: August 31, 2020

Abstract

The optimal retirement decision is an optimal stopping problem when retirement is irreversible. We investigate the optimal consumption, investment, and retirement decisions when the mean return of a risky asset is unobservable and is estimated by filtering from historical prices. To ensure non-negativity of the consumption rate and the borrowing constraints on the wealth process of the representative agent, we conduct our analysis using a duality approach. We link the dual problem to American option pricing with stochastic volatility and prove that the duality gap is closed. We then apply our theory to a hidden Markov model for regime-switching mean return with Bayesian learning or the Wonham filter. We fully characterize the existence and uniqueness of variational inequality in the dual optimal stopping problem, as well as the free boundary of the problem. An asymptotic closed-form solution is derived for optimal retirement timing by small-scale perturbation. We discuss the potential applications of the results to other partial information settings.

Keywords: voluntary retirement, portfolio optimization, optimal consumption, optimal stopping, free boundary problem, partial information

JEL Classification: G11,C61

Suggested Citation

Chen, Kexin and Jeon, Junkee and Wong, Hoi Ying, Optimal Retirement Under Partial Information (August 31, 2020). Available at SSRN: https://ssrn.com/abstract=3683553 or http://dx.doi.org/10.2139/ssrn.3683553

Kexin Chen (Contact Author)

The Chinese University of Hong Kong (CUHK) - Department of Statistics ( email )

Hung Hom
Kowloon
Hong Kong
Hong Kong

Junkee Jeon

Kyung Hee University - Department of Applied Mathematics ( email )

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

HOME PAGE: http://sites.google.com/site/junkeejeon/home

Hoi Ying Wong

The Chinese University of Hong Kong (CUHK) - Department of Statistics ( email )

Shatin, N.T.
Hong Kong

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