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Optimal retirement consumption with a stochastic force of mortality

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  • Huaxiong Huang
  • Moshe A. Milevsky
  • Thomas S. Salisbury
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    Abstract

    We extend the lifecycle model (LCM) of consumption over a random horizon (a.k.a. the Yaari model) to a world in which (i.) the force of mortality obeys a diffusion process as opposed to being deterministic, and (ii.) a consumer can adapt their consumption strategy to new information about their mortality rate (a.k.a. health status) as it becomes available. In particular, we derive the optimal consumption rate and focus on the impact of mortality rate uncertainty vs. simple lifetime uncertainty -- assuming the actuarial survival curves are initially identical -- in the retirement phase where this risk plays a greater role. In addition to deriving and numerically solving the PDE for the optimal consumption rate, our main general result is that when utility preferences are logarithmic the initial consumption rates are identical. But, in a CRRA framework in which the coefficient of relative risk aversion is greater (smaller) than one, the consumption rate is higher (lower) and a stochastic force of mortality does make a difference. That said, numerical experiments indicate that even for non-logarithmic preferences, the stochastic mortality effect is relatively minor from the individual's perspective. Our results should be relevant to researchers interested in calibrating the lifecycle model as well as those who provide normative guidance (a.k.a. financial advice) to retirees.

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    File URL: http://arxiv.org/pdf/1205.2295
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1205.2295.

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    Date of creation: May 2012
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    Publication status: Published in Insurance: Mathematics and Economics 51 (2012), pp. 282-291
    Handle: RePEc:arx:papers:1205.2295

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    1. Davies, James B, 1981. "Uncertain Lifetime, Consumption, and Dissaving in Retirement," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 89(3), pages 561-77, June.
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    16. Wills, Samuel & Sherris, Michael, 2010. "Securitization, structuring and pricing of longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 173-185, February.
    17. Geoffrey Kingston & Susan Thorp, 2004. "Annuitization and Asset Allocation with HARA Utlity," Econometric Society 2004 Australasian Meetings 248, Econometric Society.
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    Cited by:
    1. Thomas Post & Katja Hanewald, 2011. "Longevity Risk, Subjective Survival Expectations, and Individual Saving Behavior," Working Papers 201111, ARC Centre of Excellence in Population Ageing Research (CEPAR), Australian School of Business, University of New South Wales.
    2. Schendel, Lorenz S., 2014. "Consumption-investment problems with stochastic mortality risk," SAFE Working Paper Series 43, Research Center SAFE - Sustainable Architecture for Finance in Europe, Goethe University Frankfurt.
    3. Kraft, Holger & Schendel, Lorenz S. & Steffensen, Mogens, 2014. "Life insurance demand under health shock risk," SAFE Working Paper Series 40, Research Center SAFE - Sustainable Architecture for Finance in Europe, Goethe University Frankfurt.

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