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Optimal Retirement Under Partial Information

Author

Listed:
  • Kexin Chen

    (Department of Statistics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong; Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong)

  • Junkee Jeon

    (Department of Applied Mathematics, Kyung Hee University, Yongin-si, Gyeonggi-do 17104, Korea)

  • Hoi Ying Wong

    (Department of Statistics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong)

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 nonnegativity 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. 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.

Suggested Citation

  • Kexin Chen & Junkee Jeon & Hoi Ying Wong, 2022. "Optimal Retirement Under Partial Information," Mathematics of Operations Research, INFORMS, vol. 47(3), pages 1802-1832, August.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:3:p:1802-1832
    DOI: 10.1287/moor.2021.1189
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