Optimal consumption and allocation in variable annuities with Guaranteed Minimum Death Benefits
We 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.
Volume (Year): 51 (2012)
Issue (Month): 3 ()
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- 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.
- 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.
- 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 706-732, 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.
- 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.
- Jeffrey R. Brown, 1999. "Private Pensions, Mortality Risk, and the Decision to Annuitize," NBER Working Papers 7191, National Bureau of Economic Research, Inc.
- 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, 1989. "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.
- 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.
- 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, "undated". "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 & 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.
- Mariacristina De Nardi, 2004. "Wealth Inequality and Intergenerational Links," Review of Economic Studies, Oxford University Press, vol. 71(3), pages 743-768.
- 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.
- 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.
- 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.
- 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.
- 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 247-257, August.
- 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.
- 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.
- 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.
- 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.
- 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.
- Bauer, Daniel & Kling, Alexander & Russ, Jochen, 2008. "A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 38(02), pages 621-651, November. Full references (including those not matched with items on IDEAS)