Conditioning Capacities and Choquet Integrals: The Role of Comonotony
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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.
- Chateauneuf, A. (1994),Modeling attitudes towards uncertainty and risk through the use of Choquet integral, Annals of Operation Research 52, 3-20.
- Chateauneuf, A., Cohen, M. and Kast, R. (1997), Comonotone random variables in economics: A review of some results, DT GREQAM 97A07.
- Cohen, M., Gilboa, I., Jaffray, J-Y. and Schmeidler, D. (1997), An experimental study of updating ambiguous beliefs, 1st ISIPTA proceedings, Ghent, Belgium.
- Denneberg D. (1994), Non Additive Measures and Integrals. Dordrecht/ Boston/London: Kluwer Academic Publishers.
- Denneberg D. (1994), Conditionning (updating) non-additive measures, Annals of Operations Research 52, 21-42. CrossRef
- Gilboa, I. and Schmeidler, D. (1993), Updating ambiguous beliefs, Journal of Economic Theory 59, 33-49. CrossRef
- Kast, R. and Lapied, A. (1997), A decision theoretic approach to bid-ask spreads, Finance 18, 115-137.
- Schmeidler, D. (1986), Integral Mathematical representation without additivity, Proceedings of the American Mathematical Society 97, 253-261. CrossRef
- Schmeidler, D. (1989), Subjective probability and expected utility without additivity, Econometrica 57, 571-587. CrossRef
- Yaari, M. (1987), The dual theory of choice under risk, Econometrica 55, 119-132. CrossRef
- Conditioning Capacities and Choquet Integrals: The Role of Comonotony
Theory and Decision
Volume 51, Issue 2-4 , pp 367-386
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- Choquet integral
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- Conditionnal capacities
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