Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

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

  • 118 Accesses

  • 9 Citations

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 (DC) requirements and conditional capacities are derived, under some conditions on information. In contrast with other models referring to DC, ours does not collapse into a linear one because it violates a weak version of consequentialism.

This is a preview of subscription content, log in to check access.

References

  1. Chateauneuf A. (1991) On the use of capacities in modelling uncertainty aversion and risk aversion. Journal of Mathematical Economics 20: 349–369

  2. Chateauneuf A., Kast R., Lapied A. (2001) Conditioning capacities and Choquet integrals: The role of comonotony. Theory and Decision 51: 367–386

  3. Chateauneuf A., Rébillé Y. (2004) Some characterizations of non-additive multi-period models. Mathematical Social Sciences 48: 235–250

  4. de Finetti B. (1930) Fondamenti logici del raggionamento probabilistico. Bolletino dell’unione matematica italiana 9: 258–261

  5. Dempster A. (1967) Upper and lower probabilities induced by multivariated mapping. Annals of Mathematical Statistics 38: 325–339

  6. Denneberg D. (1994) Conditioning (updating) non additive measures. Annals of Operations Research 52: 21–42

  7. Diecidue E., Wakker P. (2002) Dutch Books: Avoiding strategic and dynamic complications and a comonotonic extension. Mathematical Social Sciences 43: 135–149

  8. Fagin, R., & Halpern, J. Y. (1990). A new approach to updating beliefs. Proceedings of 6th Conference on Uncertainty in Artificial Intelligence, 347–374.

  9. Ghirardato P. (1997) On independence for non-additive measures with a Fubini theorem. Journal of Economic Theory 73: 261–291

  10. Ghirardato P. (2002) Revisiting savage in a conditional world. Economic Theory 20: 83–92

  11. Gilboa I. (1989) Expectations and variations in multi-period decisions. Econometrica 57: 1153–1159

  12. Gilboa I., Schmeidler D. (1993) Updating ambiguous beliefs. Journal of Econonomic Theory 59: 33–49

  13. Hammond P. (1989) Consistent plans, consequentialism, and expected utility. Econometrica 57: 1445–1449

  14. Jaffray J.-Y. (1992) Bayesian updating and belief functions. IEE Transactions on Systems, Man and Cybernetics 22: 1144–1552

  15. Karni E., Schmeidler D. (1991) Atemporal dynamic consistency and expected utility theory. Journal of Economic Theory 54: 401–408

  16. Kast, R., Lapied, A. (2007). Dynamically consistent Choquet capacities. ICER WP: Torino.

  17. Kast, R., Lapied, A. & Toqueboeuf, P. (2007). Updating Choquet integrals, consequentialism and dynamic consistency. DT, Greqam.

  18. Koopmans, T. (1972). Representation of preference orderings over time. In C. Mac Guire, R. Radner (Eds.), Decision and organization (pp. 79–100). Amsterdam: North Holland.

  19. Lapied, A., & Toqueoeuf, P. (2007). Consistent dynamic choice and non expected utility preferences. DT, Greqam.

  20. Machina M. (1998) Dynamic consistency and non expected utility models of choice under uncertainty. Journal of Economic Literature 22: 1622–1668

  21. Nishimura, K., & Ozaki, H. (2003). A simple axiomatization of iterated Choquet objectives. W. P. CIRJE, Tokyo University.

  22. Sarin R., Wakker P. (1998) Dynamic choice and non expected utility. Journal of Risk and Uncertainty 17: 87–119

  23. Schmeidler D. (1989) Subjective probability and expected utility without additivity. Econometrica 57: 571–587

  24. Shafer W. (1967) A mathematical theory of evidence. Princeton University Press, Princeton, NJ

  25. Yaari M. (1987) The dual theory of choice under risk. Econometrica 55: 95–115

Download references

Author information

Correspondence to Robert Kast.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Kast, R., Lapied, A. Valuing future cash flows with non separable discount factors and non additive subjective measures: conditional Choquet capacities on time and on uncertainty. Theory Decis 69, 27–53 (2010). https://doi.org/10.1007/s11238-008-9107-1

Download citation

Keywords

  • Capacities
  • Comonotonicity
  • Conditional Choquet integrals
  • Conditional capacities
  • Discount factors
  • Information
  • Product spaces
  • Subjective measures

JEL Classification

  • D 81
  • D 83
  • D 92
  • G 31