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Valuing future cash flows with non separable discount factors and non additive subjective measures: conditional Choquet capacities on time and on uncertainty

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  • Robert Kast

    ()

  • André Lapied

    ()

Abstract

We consider future cash flows that are contingent both on dates in time and on uncertain states. The decision maker (DM) values the cash flows according to its decision criterion: Here the payoffs’ expectation with respect to a capacity measure. The subjective measure grasps the DM’s behaviour in front of the future, in the spirit of de Finetti’s (1930) and of Yaari’s (1987) Dual Theory in the case of risk. Decomposition of the criterion into two criteria that represent the DM’s preferences on uncertain payoffs and time contingent payoffs are derived from Ghirardato’s (1997) results. Conditional Choquet integrals are defined by dynamic consistency requirements and conditional capacities are derived, under some conditions on information. In contrast with other models referring to dynamic consistency, ours doesn’t collapse into a linear one because it violates a weak version of consequentialism.

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File URL: http://hdl.handle.net/10.1007/s11238-008-9107-1
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Bibliographic Info

Article provided by Springer in its journal Theory and Decision.

Volume (Year): 69 (2010)
Issue (Month): 1 (July)
Pages: 27-53

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Handle: RePEc:kap:theord:v:69:y:2010:i:1:p:27-53

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Web page: http://www.springerlink.com/link.asp?id=100341

Related research

Keywords: Capacities; Comonotonicity; Conditional Choquet integrals; Conditional capacities; Discount factors; Information; Product spaces; Subjective measures; D 81; D 83; D 92; G 31;

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References

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  1. Karni, Edi & Schmeidler, David, 1991. "Atemporal dynamic consistency and expected utility theory," Journal of Economic Theory, Elsevier, vol. 54(2), pages 401-408, August.
  2. Chateauneuf, Alain & Rebille, Yann, 2004. "Some characterizations of non-additive multi-period models," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 235-250, November.
  3. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-68, December.
  4. Sarin, Rakesh & Wakker, Peter P, 1998. "Dynamic Choice and NonExpected Utility," Journal of Risk and Uncertainty, Springer, vol. 17(2), pages 87-119, November.
  5. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  6. Itzhak Gilboa & David Schmeidler, 1991. "Updating Ambiguous Beliefs," Discussion Papers 924, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Ghirardato, Paolo, 1995. "On Independence For Non-Additive Measures, With a Fubini Theorem," Working Papers 940, California Institute of Technology, Division of the Humanities and Social Sciences.
  8. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  9. Robert Kast & André Lapied & Pascal Toquebeuf, 2008. "Updating Choquet Integrals , Consequentialism and Dynamic Consistency," ICER Working Papers - Applied Mathematics Series 04-2008, ICER - International Centre for Economic Research.
  10. Alain Chateauneuf & Robert Kast & André Lapied, 2001. "Conditioning Capacities and Choquet Integrals: The Role of Comonotony," Theory and Decision, Springer, vol. 51(2), pages 367-386, December.
  11. André Lapied & Pascal Toquebeuf, 2009. "Consistent dynamic choice and non-expected utility preferences," Working Papers hal-00416214, HAL.
  12. André Lapied & Pascal Tocquebeuf, 2007. "Consistent Dynamice Choice And Non-Expected Utility Preferences," Working Papers halshs-00353880, HAL.
  13. Diecidue, Enrico & Wakker, Peter P., 2002. "Dutch books: avoiding strategic and dynamic complications, and a comonotonic extension," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 135-149, March.
  14. Hammond, Peter J, 1989. "Consistent Plans, Consequentialism, and Expected Utility," Econometrica, Econometric Society, vol. 57(6), pages 1445-49, November.
  15. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer, vol. 20(1), pages 83-92.
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Cited by:
  1. Robert Kast & André Lapied, 2010. "Dynamically consistent Choquet random walk and real investments," Working Papers halshs-00533826, HAL.

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