Optimal retirement consumption with a stochastic force of mortality
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.
|Date of creation:||May 2012|
|Date of revision:|
|Publication status:||Published in Insurance: Mathematics and Economics 51 (2012), pp. 282-291|
|Contact details of provider:|| Web page: http://arxiv.org/|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
- Wills, Samuel & Sherris, Michael, 2010. "Securitization, structuring and pricing of longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 173-185, February.
- Leung, Siu Fai, 1994.
"Uncertain Lifetime, the Theory of the Consumer, and the Life Cycle Hypothesis,"
Econometric Society, vol. 62(5), pages 1233-39, September.
- Leung, S.F., 1992. "Uncertain Lifetime, the Theory of the Consumer, and the Life Cycle Hypothesis," RCER Working Papers 323, University of Rochester - Center for Economic Research (RCER).
- Richard, Scott F., 1975. "Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model," Journal of Financial Economics, Elsevier, vol. 2(2), pages 187-203, June.
- Deaton, A., 1989.
"Saving And Liquidity Constraints,"
153, Princeton, Woodrow Wilson School - Public and International Affairs.
- repec:dau:papers:123456789/4812 is not listed on IDEAS
- Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
- Lachance, Marie-Eve, 2012. "Optimal onset and exhaustion of retirement savings in a life-cycle model," Journal of Pension Economics and Finance, Cambridge University Press, vol. 11(01), pages 21-52, January.
- Antoine Bommier & Bertrand Villeneuve, 2010.
"Risk Aversion and the Value of Risk to Life,"
CER-ETH Economics working paper series
10/133, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
- Davies, James B, 1981. "Uncertain Lifetime, Consumption, and Dissaving in Retirement," Journal of Political Economy, University of Chicago Press, vol. 89(3), pages 561-77, June.
- Menoncin, Francesco, 2008.
"The role of longevity bonds in optimal portfolios,"
Insurance: Mathematics and Economics,
Elsevier, vol. 42(1), pages 343-358, February.
- Bodie, Zvi & Detemple, Jerome B. & Otruba, Susanne & Walter, Stephan, 2004. "Optimal consumption-portfolio choices and retirement planning," Journal of Economic Dynamics and Control, Elsevier, vol. 28(6), pages 1115-1148, March.
- Andrew J. G. Cairns & David Blake & Kevin Dowd, 2006. "A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 687-718.
- Kingston, Geoffrey & Thorp, Susan, 2005.
"Annuitization and asset allocation with HARA utility,"
Journal of Pension Economics and Finance,
Cambridge University Press, vol. 4(03), pages 225-248, November.
- Geoffrey Kingston & Susan Thorp, 2004. "Annuitization and Asset Allocation with HARA Utlity," Econometric Society 2004 Australasian Meetings 248, Econometric Society.
- Levhari, David & Mirman, Leonard J, 1977. "Savings and Consumption with an Uncertain Horizon," Journal of Political Economy, University of Chicago Press, vol. 85(2), pages 265-81, April.
- Bauer Daniel & Börger Matthias & Ruß Jochen & Zwiesler Hans-Joachim, 2008. "The Volatility of Mortality," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 3(1), pages 1-29, September.
- Park, Myung-Ho, 2006. "An analytical solution to the inverse consumption function with liquidity constraints," Economics Letters, Elsevier, vol. 92(3), pages 389-394, September.
- Orazio P. Attanasio & Guglielmo Weber, 2010.
"Consumption and Saving: Models of Intertemporal Allocation and Their Implications for Public Policy,"
Journal of Economic Literature,
American Economic Association, vol. 48(3), pages 693-751, September.
- Orazio P. Attanasio & Guglielmo Weber, 2010. "Consumption and Saving: Models of Intertemporal Allocation and Their Implications for Public Policy," NBER Working Papers 15756, National Bureau of Economic Research, Inc.
- Post Thomas, 2012. "Individual Welfare Gains from Deferred Life-Annuities under Stochastic Mortality," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 6(2), pages 1-26, June.
- Feigenbaum, James, 2008. "Can mortality risk explain the consumption hump?," Journal of Macroeconomics, Elsevier, vol. 30(3), pages 844-872, September.
- Dothan, L. Uri, 1978. "On the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 6(1), pages 59-69, March.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1205.2295. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If references are entirely missing, you can add them using this form.