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Optimal Time to Enter a Retirement Village

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  • Jinhui Zhang

    (Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia
    Current address: 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)

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.

Suggested Citation

  • Jinhui Zhang & Sachi Purcal & Jiaqin Wei, 2017. "Optimal Time to Enter a Retirement Village," Risks, MDPI, Open Access Journal, vol. 5(1), pages 1-20, March.
  • Handle: RePEc:gam:jrisks:v:5:y:2017:i:1:p:20-:d:93729
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    References listed on IDEAS

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