Optimal consumption and allocation in variable annuities with Guaranteed Minimum Death Benefits
AbstractWe determine the optimal allocation of funds between the fixed and variable subaccounts in a variable annuity with a GMDB (Guaranteed Minimum Death Benefit) clause featuring partial withdrawals by using a utility-based approach. The Merton method is applied by assuming that individuals allocate funds optimally in order to maximize the expected utility of lifetime consumption. It also reflects bequest motives by including the recipient’s utility in terms of the policyholder’s guaranteed death benefits. We derive the optimal transfer choice by the insured, and furthermore price the GMDB through maximizing the discounted expected utility of the policyholders and beneficiaries by investing dynamically in the fixed account and variable fund and withdrawing optimally.
Download InfoIf 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.
Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 51 (2012)
Issue (Month): 3 ()
Contact details of provider:
Web page: http://www.elsevier.com/locate/inca/505554
GMDB; Variable annuity; Merton model; Expected utility;
Find related papers by JEL classification:
- D91 - Microeconomics - - Intertemporal Choice - - - Intertemporal Household Choice; Life Cycle Models and Saving
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.:
- Bernheim, B Douglas, 1991.
"How Strong Are Bequest Motives? Evidence Based on Estimates of the Demand for Life Insurance and Annuities,"
Journal of Political Economy,
University of Chicago Press, vol. 99(5), pages 899-927, October.
- B. Douglas Bernheim, 1992. "How Strong are Bequest Motives? Evidence Based on Estimates of the Demand for Life Insurance and Annuities," NBER Working Papers 2942, National Bureau of Economic Research, Inc.
- 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.
- 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.
- Mariacristina Nardi, 2004.
"Wealth Inequality and Intergenerational Links,"
Review of Economic Studies,
Wiley Blackwell, vol. 71, pages 743-768, 07.
- Mariacristina deNardi, 2000. "Wealth Inequality and Intergenerational Links," Econometric Society World Congress 2000 Contributed Papers 0547, Econometric Society.
- Mariacristina De Nardi, 2002. "Wealth inequality and intergenerational links," Staff Report 314, Federal Reserve Bank of Minneapolis.
- Coleman, Thomas F. & Li, Yuying & Patron, Maria-Cristina, 2006. "Hedging guarantees in variable annuities under both equity and interest rate risks," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 215-228, April.
- Tim Leung & Ronnie Sircar, 2009. "Accounting For Risk Aversion, Vesting, Job Termination Risk And Multiple Exercises In Valuation Of Employee Stock Options," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 99-128.
- Min Dai & Yue Kuen Kwok & Jianping Zong, 2008. "Guaranteed Minimum Withdrawal Benefit In Variable Annuities," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 595-611.
- Jeffrey R. Brown, 1999.
"Private Pensions, Mortality Risk, and the Decision to Annuitize,"
NBER Working Papers
7191, National Bureau of Economic Research, Inc.
- Brown, Jeffrey R., 2001. "Private pensions, mortality risk, and the decision to annuitize," Journal of Public Economics, Elsevier, vol. 82(1), pages 29-62, October.
- Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August.
- David Blake & Andrew J. G. Cairns & Kevin Dowd, 2003.
"Pensionmetrics 2: stochastic pension plan design during the distribution phase,"
LSE Research Online Documents on Economics
24830, London School of Economics and Political Science, LSE Library.
- Blake, David & Cairns, Andrew J. G. & Dowd, Kevin, 2003. "Pensionmetrics 2: stochastic pension plan design during the distribution phase," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 29-47, August.
- Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(01), pages 1-12, March.
- Charupat, Narat & Milevsky, Moshe A., 2002. "Optimal asset allocation in life annuities: a note," Insurance: Mathematics and Economics, Elsevier, vol. 30(2), pages 199-209, April.
- 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.
- 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.
- Eric R. Ulm, 2006. "The Effect of the Real Option to Transfer on the Value of Guaranteed Minimum Death Benefits," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(1), pages 43-69.
- 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.
- A. C. Belanger & P. A. Forsyth & G. Labahn, 2009. "Valuing the Guaranteed Minimum Death Benefit Clause with Partial Withdrawals," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(6), pages 451-496.
- John Ameriks & Andrew Caplin & Steven Laufer & Stijn Van Nieuwerburgh, 2011. "The Joy of Giving or Assisted Living? Using Strategic Surveys to Separate Public Care Aversion from Bequest Motives," Journal of Finance, American Finance Association, vol. 66(2), pages 519-561, 04.
- Chen, Z. & Vetzal, K. & Forsyth, P.A., 2008. "The effect of modelling parameters on the value of GMWB guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 165-173, August.
- Huang, H. & Milevsky, M.A. & Salisbury, T.S., 2014. "Optimal initiation of a GLWB in a variable annuity: No Arbitrage approach," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 102-111.
- Gan, Guojun, 2013. "Application of data clustering and machine learning in variable annuity valuation," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 795-801.
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.