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.:
- Antoine Bommier & Bertrand Villeneuve, 2004.
"Risk Aversion and the Value of Risk to Life,"
CESifo Working Paper Series
1267, CESifo Group Munich.
- 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.
- Bommier, Antoine & Villeneuve, Bertrand, 2008. "Risk Aversion and the Value of Risk to Life," MPRA Paper 11943, University Library of Munich, Germany.
- Geoffrey Kingston & Susan Thorp, 2004.
"Annuitization and Asset Allocation with HARA Utlity,"
Econometric Society 2004 Australasian Meetings
248, Econometric Society.
- 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.
- Angus Deaton, 1989.
"Saving and Liquidity Constraints,"
NBER Working Papers
3196, National Bureau of Economic Research, Inc.
- 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.
- 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).
- 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.
- 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.
- 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.
- 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.
- 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.
- Dothan, L. Uri, 1978. "On the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 6(1), pages 59-69, March.
- repec:dau:papers:123456789/4812 is not listed on IDEAS
- Feigenbaum, James, 2008. "Can mortality risk explain the consumption hump?," Journal of Macroeconomics, Elsevier, vol. 30(3), pages 844-872, September.
- 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.
- 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.
- 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.
- 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.
- Wills, Samuel & Sherris, Michael, 2010. "Securitization, structuring and pricing of longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 173-185, February.
- 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.
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.