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A rank-dependent utility model of uncertain lifetime, time consistency and life insurance

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  • Nicolas Drouhin

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, ENS Cachan - École Normale Supérieure de Cachan - École normale supérieure (ENS) - Cachan)

Abstract

In a continuous time life cycle model of consumption with uncertain lifetime and no ''pure time preference", we use a non-parametric specification of rank dependent utility theory to characterize the preferences of the agents. From normative point of view, the paper discusses the implication of adding an axiom of time consistency to the former model. We prove that time consistency holds for a much wider class of probability weighting functions than the identity one characterizing the expected utility model. This special class of probability weighting functions provides foundations for a constant subjective rate of discount which interact multiplicatively with the instantaneous conditional probability of dying. We show that even if agent are time consistent, life annuities no more provide perfect insurance against the risk to live.

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Bibliographic Info

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00748662.

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Date of creation: 13 Nov 2012
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Handle: RePEc:hal:cesptp:halshs-00748662

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Keywords: intertemporal choice; life cycle theory of consumption and saving; uncertain lifetime; life insurance; time consistency; rank dependent utility.;

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  1. Richard Zeckhauser & W. Viscusi, 2008. "Discounting dilemmas: Editors’ introduction," Journal of Risk and Uncertainty, Springer, Springer, vol. 37(2), pages 95-106, December.
  2. Leung, Siu Fai, 1994. "Uncertain Lifetime, the Theory of the Consumer, and the Life Cycle Hypothesis," Econometrica, Econometric Society, Econometric Society, vol. 62(5), pages 1233-39, September.
  3. Peter D Sozou, 2003. "On Hyperbolic Discounting and Uncertain Hazard Rates," Levine's Working Paper Archive 618897000000000775, David K. Levine.
  4. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, Elsevier, vol. 8(3), pages 201-207.
  5. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, Econometric Society, vol. 55(1), pages 95-115, January.
  6. Halevy, Yoram, 2004. "Strotz meets Allais: Diminishing Impatience and the Certainty Effect," Microeconomics.ca working papers, Vancouver School of Economics halevy-04-10-29-10-08-43, Vancouver School of Economics, revised 25 Feb 2014.
  7. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 3(4), pages 323-343, December.
  8. Enrico Diecidue & Ulrich Schmidt & Horst Zank, 2006. "Parametric Weighting Functions," The School of Economics Discussion Paper Series, Economics, The University of Manchester 0622, Economics, The University of Manchester.
  9. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
  10. Laibson, David, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 112(2), pages 443-77, May.
  11. Nicolas Drouhin, 2001. "Lifetime Uncertainty and Time Preference," Theory and Decision, Springer, Springer, vol. 51(2), pages 145-172, December.
  12. Antoine Bommier, 2001. "Uncertain lifetime and intertemporal choice : risk aversion as a rationale for time discounting," Research Unit Working Papers, Laboratoire d'Economie Appliquee, INRA 0108, Laboratoire d'Economie Appliquee, INRA.
  13. Moresi, Serge, 1999. "Uncertain lifetime, risk aversion and intertemporal substitution," Economics Letters, Elsevier, Elsevier, vol. 62(2), pages 207-212, February.
  14. Loewenstein, George & Prelec, Drazen, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 107(2), pages 573-97, May.
  15. Partha Dasgupta & Eric Maskin, 2004. "Uncertainty and Hyperbolic Discounting," Economics Working Papers, Institute for Advanced Study, School of Social Science 0023, Institute for Advanced Study, School of Social Science.
  16. Bleichrodt, Han & Eeckhoudt, Louis, 2006. "Survival risks, intertemporal consumption, and insurance: The case of distorted probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 335-346, April.
  17. Alexander Ludwig & Alexander Zimper, 2007. "A Parsimonious Model of Subjective Life Expectancy," MEA discussion paper series, Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy 07154, Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy.
  18. Nicolas Drouhin, 2009. "Hyperbolic discounting may be time consistent," Economics Bulletin, AccessEcon, vol. 29(4), pages 2549-2555.
  19. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, Springer, vol. 5(4), pages 297-323, October.
  20. Alexander Zimper & Alexander Ludwig & Max Groneck, 2012. "A Life-Cycle Consumption Model with Ambiguous Survival Beliefs," 2012 Meeting Papers, Society for Economic Dynamics 693, Society for Economic Dynamics.
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