Optimal Time to Enter a Retirement Village

Jinhui Zhang, Sachi Purcal and Jiaqin Wei
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Jinhui Zhang: Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia
Sachi Purcal: Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia
Jiaqin Wei: School of Statistics, Faculty of Economics and Management, East China Normal University, Shanghai 200241, China

Risks, 2017, vol. 5, issue 1, 1-20

Abstract: We consider the financial planning problem of a retiree wishing to enter a retirement village at a future uncertain date. The date of entry is determined by the retiree’s utility and bequest maximisation problem within the context of uncertain future health states. In addition, the retiree must choose optimal consumption, investment, bequest and purchase of insurance products prior to their full annuitisation on entry to the retirement village. A hyperbolic absolute risk-aversion (HARA) utility function is used to allow necessary consumption for basic living and medical costs. The retirement village will typically require an initial deposit upon entry. This threshold wealth requirement leads to exercising the replication of an American put option at the uncertain stopping time. From our numerical results, active insurance and annuity markets are shown to be a critical aspect in retirement planning.

Keywords: retirement village; optimal control; optimal stopping, HARA, American put option; long-term care needs, costs and products for the elderly; disability/health state transitions; life-cycle modelling related to the retirement phase (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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