Theory and Decision

, Volume 51, Issue 2–4, pp 367–386

Conditioning Capacities and Choquet Integrals: The Role of Comonotony

  • Alain Chateauneuf
  • Robert Kast
  • André Lapied
Article

Abstract

Choquet integrals and capacities play a crucial role in modern decision theory. Comonotony is a central concept for these theories because the main property of a Choquet integral is its additivity for comonotone functions. We consider a Choquet integral representation of preferences showing uncertainty aversion (pessimism) and propose axioms on time consistency which yield a candidate for conditional Choquet integrals. An other axiom characterizes the role of comonotony in the use of information. We obtain two conditioning rules for capacities which amount to the well-known Bayes' and Dempster–Schafer's updating rules. We are allowed to interpret both of them as a lack of confidence in information in a dynamic extension of pessimism.

Choquet integral Comonotony Time consitency Conditionnal capacities 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. Chateauneuf, A. (1994),Modeling attitudes towards uncertainty and risk through the use of Choquet integral, Annals of Operation Research 52, 3-20.Google Scholar
  2. Chateauneuf, A., Cohen, M. and Kast, R. (1997), Comonotone random variables in economics: A review of some results, DT GREQAM 97A07.Google Scholar
  3. Cohen, M., Gilboa, I., Jaffray, J-Y. and Schmeidler, D. (1997), An experimental study of updating ambiguous beliefs, 1st ISIPTA proceedings, Ghent, Belgium.Google Scholar
  4. Denneberg D. (1994), Non Additive Measures and Integrals. Dordrecht/ Boston/London: Kluwer Academic Publishers.Google Scholar
  5. Denneberg D. (1994), Conditionning (updating) non-additive measures, Annals of Operations Research 52, 21-42.CrossRefGoogle Scholar
  6. Gilboa, I. and Schmeidler, D. (1993), Updating ambiguous beliefs, Journal of Economic Theory 59, 33-49.CrossRefGoogle Scholar
  7. Kast, R. and Lapied, A. (1997), A decision theoretic approach to bid-ask spreads, Finance 18, 115-137.Google Scholar
  8. Schmeidler, D. (1986), Integral Mathematical representation without additivity, Proceedings of the American Mathematical Society 97, 253-261.CrossRefGoogle Scholar
  9. Schmeidler, D. (1989), Subjective probability and expected utility without additivity, Econometrica 57, 571-587.CrossRefGoogle Scholar
  10. Yaari, M. (1987), The dual theory of choice under risk, Econometrica 55, 119-132.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Alain Chateauneuf
    • 1
  • Robert Kast
    • 1
  • André Lapied
    • 1
  1. 1.CERMSEMUniversité de Paris IParisFrance

Personalised recommendations