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Risks 2017, 5(1), 20; doi:10.3390/risks5010020

Optimal Time to Enter a Retirement Village

1
Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia
2
School of Statistics, Faculty of Economics and Management, East China Normal University, Shanghai 200241, China
3
Current address: Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia.
*
Author to whom correspondence should be addressed.
Academic Editor: Pavel Shevchenko
Received: 14 October 2016 / Revised: 23 January 2017 / Accepted: 18 March 2017 / Published: 22 March 2017
(This article belongs to the Special Issue Ageing Population Risks)
View Full-Text   |   Download PDF [455 KB, uploaded 22 March 2017]   |  

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. View Full-Text
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 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
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Zhang, J.; Purcal, S.; Wei, J. Optimal Time to Enter a Retirement Village. Risks 2017, 5, 20.

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