Optimal consumption and portfolio choice for pooled annuity funds
This paper presents the optimal continuous time dynamic consumption and portfolio choice for pooled annuity funds. A pooled annuity fund constitutes an alternative way to protect against mortality risk compared to purchasing a life annuity. The crucial difference between the pooled annuity fund and purchase of a life annuity offered by an insurance company is that participants of a pooled annuity fund still have to bear some mortality risk while insured annuitants bear no mortality risk at all. The population of the pool is modelled by employing a Poisson process with time-dependent hazard-rate. It follows that the pool member's optimization problem has to account for the stochastic investment horizon and for jumps in wealth which occur if another pool member dies. In case the number of pool members goes to infinity analytical solutions are provided. For finite pool sizes the solution of the optimization problem is reduced to the numerical solution of a set of ODEs. A simulation and welfare analysis show that pooled annuity funds insure very effectively against longevity risk even if their pool size is rather small. Only very risk averse investors or those without access to small pools are more inclined to pay a risk premium to access private life annuity markets in order to lay off mortality risk completely. As even families constitute such small pools the model provides theoretical justification for the low empirical annuity demand.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
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.:
- Olivia S. Mitchell & James M. Poterba & Mark J. Warshawsky, .
"New Evidence on the Money's Worth of Individual Annuities,"
Pension Research Council Working Papers
97-9, Wharton School Pension Research Council, University of Pennsylvania.
- Olivia S. Mitchell, 1999. "New Evidence on the Money's Worth of Individual Annuities," American Economic Review, American Economic Association, vol. 89(5), pages 1299-1318, December.
- Olivia S. Mitchell & James M. Poterba & Mark J. Warshawsky, 1997. "New Evidence on the Money's Worth of Individual Annuities," NBER Working Papers 6002, National Bureau of Economic Research, Inc.
- Milevsky, Moshe Arye & Ho, Kwok & Robinson, Chris, 1997. " Asset Allocation via the Conditional First Exit Time or How to Avoid Outliving Your Money," Review of Quantitative Finance and Accounting, Springer, vol. 9(1), pages 53-70, July.
- Andrew B. Abel & Mark Warshawsky, 1987.
"Specification of the Joy of Giving: Insights from Altruism,"
NBER Working Papers
2154, National Bureau of Economic Research, Inc.
- Abel, Andrew B & Warshawsky, Mark, 1988. "Specification of the Joy of Giving: Insights from Altruism," The Review of Economics and Statistics, MIT Press, vol. 70(1), pages 145-49, February.
- Andrew B. Abel & Mark Warshawsky, . "Specification of the Joy of Giving: Insights from Altruism," Rodney L. White Center for Financial Research Working Papers 3-87, Wharton School Rodney L. White Center for Financial Research.
- Andrew B. Abel & Mark Warshawsky, . "Specification of the Joy of Giving: Insights from Altruism," Rodney L. White Center for Financial Research Working Papers 03-87, Wharton School Rodney L. White Center for Financial Research.
- Andrew J. G. Cairns & David Blake & Kevin Dowd, 2004.
"Stochastic lifestyling: optimal dynamic asset allocation for defined contribution pension plans,"
LSE Research Online Documents on Economics
24831, London School of Economics and Political Science, LSE Library.
- Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans," Journal of Economic Dynamics and Control, Elsevier, vol. 30(5), pages 843-877, May.
- Laurence J. Kotlikoff & Lawrence H. Summers, 1980.
"The Role of Intergenerational Transfers in Aggregate Capital Accumulation,"
NBER Working Papers
0445, National Bureau of Economic Research, Inc.
- Kotlikoff, Laurence J & Summers, Lawrence H, 1981. "The Role of Intergenerational Transfers in Aggregate Capital Accumulation," Journal of Political Economy, University of Chicago Press, vol. 89(4), pages 706-32, August.
- Thomas Davidoff & Jeffrey R. Brown & Peter A. Diamond, 2005.
"Annuities and Individual Welfare,"
American Economic Review,
American Economic Association, vol. 95(5), pages 1573-1590, December.
- Bernheim, B Douglas & Shleifer, Andrei & Summers, Lawrence H, 1986.
"The Strategic Bequest Motive,"
Journal of Labor Economics,
University of Chicago Press, vol. 4(3), pages S151-82, July.
- Horneff, Wolfram J. & Maurer, Raimond H. & Mitchell, Olivia S. & Dus, Ivica, 2008. "Following the rules: Integrating asset allocation and annuitization in retirement portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 396-408, February.
- Wolfram J. Horneff & Raimond H. Maurer & Olivia S. Mitchell & Michael Z. Stamos, 2007.
"Money in Motion: Dynamic Portfolio Choice in Retirement,"
NBER Working Papers
12942, National Bureau of Economic Research, Inc.
- Horneff, Wolfram J. & Maurer, Raimond H. & Mitchell, Olivia S. & Stamos, Michael Z., 2007. "Money in motion: Dynamic portfolio choice in retirement," CFS Working Paper Series 2007/21, Center for Financial Studies (CFS).
- Wolfram Horneff & Raimond Maurer & Olivia Mitchell & Michael Stamos, 2007. "Money in Motion: Dynamic Portfolio Choice in Retirement," Working Papers wp152, University of Michigan, Michigan Retirement Research Center.
- Hurd, Michael D, 1989. "Mortality Risk and Bequests," Econometrica, Econometric Society, vol. 57(4), pages 779-813, July.
- Francisco Gomes & Alexander Michaelides, 2005.
"Optimal Life-Cycle Asset Allocation: Understanding the Empirical Evidence,"
Journal of Finance,
American Finance Association, vol. 60(2), pages 869-904, 04.
- Gomes, Francisco J & Michaelides, Alexander, 2005. "Optimal Life-Cycle Asset Allocation: Understanding the Empirical Evidence," CEPR Discussion Papers 4853, C.E.P.R. Discussion Papers.
- Hato Schmeiser & Thomas Post, 2005. "Life Annuity Insurance Versus Self-Annuitization: An Analysis From the Perspective of the Family," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 8(2), pages 239-255, 09.
- Joao F. Cocco, 2005. "Consumption and Portfolio Choice over the Life Cycle," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 491-533.
- R. C. Merton, 1970.
"Optimum Consumption and Portfolio Rules in a Continuous-time Model,"
58, Massachusetts Institute of Technology (MIT), Department of Economics.
- Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
- Albrecht, Peter & Maurer, Raimond, 2002. "Self-Annuitization, Consumption Shortfall in Retirement and Asset Allocation: The Annuity Benchmark," Journal of Pension Economics and Finance, Cambridge University Press, vol. 1(03), pages 269-288, November.
- Wolfram Horneff & Raimond Maurer & Michael Stamos, 2006. "Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal?," Working Papers wp146, University of Michigan, Michigan Retirement Research Center.
- Ho, Kwok & Milevsky, Moshe Arye & Robinson, Chris, 1994. "Asset allocation, life expectancy and shortfall," Financial Services Review, Elsevier, vol. 3(2), pages 109-126.
- Hurd, Michael D, 1987. "Savings of the Elderly and Desired Bequests," American Economic Review, American Economic Association, vol. 77(3), pages 298-312, June.
- 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.
- Valdez, Emiliano A. & Piggott, John & Wang, Liang, 2006. "Demand and adverse selection in a pooled annuity fund," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 251-266, October.
- Albrecht, Peter & Maurer, Raimond, 2001. "Self-Annuitization, Ruin Risk in Retirement and Asset Allocation: The Annuity Benchmark," Sonderforschungsbereich 504 Publications 01-35, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:43:y:2008:i:1:p:56-68. 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: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.