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

  • 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)

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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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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  1. Zank, Horst & Schmidt, Ulrich & Diecidue, Enrico, 2007. "Parametric Weighting Functions," Economics Working Papers 2007,01, Christian-Albrechts-University of Kiel, Department of Economics.
  2. A. Ludwig & A. Zimper, 2013. "A parsimonious model of subjective life expectancy," Theory and Decision, Springer, vol. 75(4), pages 519-541, October.
  3. Peter D Sozou, 2003. "On Hyperbolic Discounting and Uncertain Hazard Rates," Levine's Working Paper Archive 618897000000000775, David K. Levine.
  4. Yoram Halevy, 2008. "Strotz Meets Allais: Diminishing Impatience and the Certainty Effect," American Economic Review, American Economic Association, vol. 98(3), pages 1145-62, June.
  5. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  6. Leung, S.F., 1992. "Uncertain Lifetime, the Theory of the Consumer, and the Life Cycle Hypothesis," RCER Working Papers 323, University of Rochester - Center for Economic Research (RCER).
  7. Antoine Bommier, 2006. "Uncertain Lifetime And Intertemporal Choice: Risk Aversion As A Rationale For Time Discounting," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(4), pages 1223-1246, November.
  8. Partha Dasgupta & Eric Maskin, 2005. "Uncertainty and Hyperbolic Discounting," American Economic Review, American Economic Association, vol. 95(4), pages 1290-1299, September.
  9. Moresi, Serge, 1999. "Uncertain lifetime, risk aversion and intertemporal substitution," Economics Letters, Elsevier, vol. 62(2), pages 207-212, February.
  10. 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.
  11. Nicolas Drouhin, 2001. "Lifetime Uncertainty and Time Preference," Theory and Decision, Springer, vol. 51(2), pages 145-172, December.
  12. 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.
  13. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
  14. Loewenstein, George & Prelec, Drazen, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, MIT Press, vol. 107(2), pages 573-97, May.
  15. Alexander Zimper & Alexander Ludwig & Max Groneck, 2012. "A Life-Cycle Consumption Model with Ambiguous Survival Beliefs," 2012 Meeting Papers 693, Society for Economic Dynamics.
  16. Richard Zeckhauser & W. Viscusi, 2008. "Discounting dilemmas: Editors’ introduction," Journal of Risk and Uncertainty, Springer, vol. 37(2), pages 95-106, December.
  17. Laibson, David, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, MIT Press, vol. 112(2), pages 443-77, May.
  18. Nicolas Drouhin, 2009. "Hyperbolic discounting may be time consistent," Economics Bulletin, , vol. 29(4), pages 2549-2555.
  19. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  20. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
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