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The annuity puzzle and consumption hump under ambiguous life expectancy

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  • Han, Nan-Wei
  • Hung, Mao-Wei
Abstract
We establish a continuous-time model to solve the optimal consumption-saving problem with life annuity. The decision-maker has ambiguous beliefs in the force of mortality and is averse to this model uncertainty. The ambiguity aversion is represented by the max-min principle under the framework of robust control. We show that the optimal annuity demand decreases with the extent of ambiguity aversion, bequest motives, and extent of relative risk aversion. For an individual with non-zero bequest motives, the optimal annuity demand becomes zero when the extent of ambiguity aversion exceeds a certain threshold. We also show that, even if the individual has access to actuarially fair annuities, the optimal consumption would have a hump-shaped path when the individual is ambiguity-averse.

Suggested Citation

  • Han, Nan-Wei & Hung, Mao-Wei, 2021. "The annuity puzzle and consumption hump under ambiguous life expectancy," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 76-88.
    • Handle: RePEc:eee:insuma:v:100:y:2021:i:c:p:76-88
    DOI: 10.1016/j.insmatheco.2021.04.011
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    as
    1. Antoine Bommier, Francois Le Grand, "undated". "Too Risk Averse to Purchase Insurance? A Theoretical Glance at the Annuity Puzzle," Working Papers ETH-RC-12-002, ETH Zurich, Chair of Systems Design.
    2. Antoine Bommier & François Le Grand, 2014. "Too risk averse to purchase insurance?," Post-Print hal-02313181, HAL.
    3. Jesus Fernández-Villaverde & Dirk Krueger, 2007. "Consumption over the Life Cycle: Facts from Consumer Expenditure Survey Data," The Review of Economics and Statistics, MIT Press, vol. 89(3), pages 552-565, August.
    4. Jeffrey R. Brown & Jeffrey R. Kling & Sendhil Mullainathan & Marian V. Wrobel, 2008. "Why Don’t People Insure Late-Life Consumption? A Framing Explanation of the Under-Annuitization Puzzle," American Economic Review, American Economic Association, vol. 98(2), pages 304-309, May.
    5. Attanasio, Orazio P, et al, 1999. "Humps and Bumps in Lifetime Consumption," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 22-35, January.
    6. Modigliani, Franco, 1986. "Life Cycle, Individual Thrift, and the Wealth of Nations," American Economic Review, American Economic Association, vol. 76(3), pages 297-313, June.
    7. 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.
    8. Branger, Nicole & Larsen, Linda Sandris & Munk, Claus, 2013. "Robust portfolio choice with ambiguity and learning about return predictability," Journal of Banking & Finance, Elsevier, vol. 37(5), pages 1397-1411.
    9. 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.
    10. repec:hal:pseose:hal-00670320 is not listed on IDEAS
    11. Holger Kraft & Claus Munk & Frank Thomas Seifried & Sebastian Wagner, 2017. "Consumption habits and humps," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(2), pages 305-330, August.
    12. Drouhin, Nicolas, 2015. "A rank-dependent utility model of uncertain lifetime," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 208-224.
    13. Raman Uppal & Tan Wang, 2003. "Model Misspecification and Underdiversification," Journal of Finance, American Finance Association, vol. 58(6), pages 2465-2486, December.
    14. Attanasio, Orazio P & Browning, Martin, 1995. "Consumption over the Life Cycle and over the Business Cycle," American Economic Review, American Economic Association, vol. 85(5), pages 1118-1137, December.
    15. Thurow, Lester C, 1969. "The Optimum Lifetime Distribution of Consumption Expenditures," American Economic Review, American Economic Association, vol. 59(3), pages 324-330, June.
    16. Hippolyte d’Albis & Emmanuel Thibault, 2018. "Ambiguous life expectancy and the demand for annuities," Theory and Decision, Springer, vol. 85(3), pages 303-319, October.
    17. repec:dau:papers:123456789/9807 is not listed on IDEAS
    18. Feigenbaum, James, 2008. "Can mortality risk explain the consumption hump?," Journal of Macroeconomics, Elsevier, vol. 30(3), pages 844-872, September.
    19. Milevsky, Moshe A. & Young, Virginia R., 2007. "Annuitization and asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 31(9), pages 3138-3177, September.
    20. Jun Liu, 2005. "An Equilibrium Model of Rare-Event Premia and Its Implication for Option Smirks," The Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 131-164.
    21. Pascal J. Maenhout, 2004. "Robust Portfolio Rules and Asset Pricing," The Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 951-983.
    22. Lars Peter Hansen & Thomas J Sargent, 2014. "A Quartet of Semigroups for Model Specification, Robustness, Prices of Risk, and Model Detection," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 4, pages 83-143, World Scientific Publishing Co. Pte. Ltd..
    23. Fernández-Villaverde, Jesús & Krueger, Dirk, 2011. "Consumption And Saving Over The Life Cycle: How Important Are Consumer Durables?," Macroeconomic Dynamics, Cambridge University Press, vol. 15(5), pages 725-770, November.
    24. Gary Hansen & Selahattin Imrohoroglu, 2008. "Consumption over the Life Cycle: The Role of Annuities," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(3), pages 566-583, July.
    25. Gan, Li & Gong, Guan & Hurd, Michael & McFadden, Daniel, 2015. "Subjective mortality risk and bequests," Journal of Econometrics, Elsevier, vol. 188(2), pages 514-525.
    26. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    27. Heckman, James J, 1974. "Life Cycle Consumption and Labor Supply: An Explanation of the Relationship Between Income and Consumption Over the Life Cycle," American Economic Review, American Economic Association, vol. 64(1), pages 188-194, March.
    28. Campbell, Ritchie A, 1980. "The Demand for Life Insurance: An Application of the Economics of Uncertainty," Journal of Finance, American Finance Association, vol. 35(5), pages 1155-1172, December.
    29. d’Albis, Hippolyte & Thibault, Emmanuel, 2012. "Optimal annuitization, uncertain survival probabilities, and maxmin preferences," Economics Letters, Elsevier, vol. 115(2), pages 296-299.
    30. Shlomo Benartzi & Alessandro Previtero & Richard H. Thaler, 2011. "Annuitization Puzzles," Journal of Economic Perspectives, American Economic Association, vol. 25(4), pages 143-164, Fall.
    31. Martin Salm, 2010. "Subjective mortality expectations and consumption and saving behaviours among the elderly," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 43(3), pages 1040-1057, August.
    32. Pierre-Olivier Gourinchas & Jonathan A. Parker, 2002. "Consumption Over the Life Cycle," Econometrica, Econometric Society, vol. 70(1), pages 47-89, January.
    33. Jeffrey R. Brown, 2007. "Rational and Behavioral Perspectives on the Role of Annuities in Retirement Planning," NBER Working Papers 13537, National Bureau of Economic Research, Inc.
    34. Zhu, Wenge, 2011. "Ambiguity aversion and an intertemporal equilibrium model of catastrophe-linked securities pricing," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 38-46, July.
    35. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    36. Horneff, Wolfram J. & Maurer, Raimond H. & Stamos, Michael Z., 2008. "Life-cycle asset allocation with annuity markets," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3590-3612, November.
    37. Barro, Robert J & Friedman, James W, 1977. "On Uncertain Lifetimes," Journal of Political Economy, University of Chicago Press, vol. 85(4), pages 843-849, August.
    38. Felix Reichling & Kent Smetters, 2015. "Optimal Annuitization with Stochastic Mortality and Correlated Medical Costs," American Economic Review, American Economic Association, vol. 105(11), pages 3273-3320, November.
    39. Bullard, James & Feigenbaum, James, 2007. "A leisurely reading of the life-cycle consumption data," Journal of Monetary Economics, Elsevier, vol. 54(8), pages 2305-2320, November.
    40. Antoine Bommier & François Grand, 2014. "Too risk averse to purchase insurance?," Journal of Risk and Uncertainty, Springer, vol. 48(2), pages 135-166, April.
    41. Lee Lockwood, 2012. "Bequest Motives and the Annuity Puzzle," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(2), pages 226-243, April.
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    2. Park, Kyunghyun & Wong, Hoi Ying & Yan, Tingjin, 2023. "Robust retirement and life insurance with inflation risk and model ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 1-30.

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