Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-15T15:31:01.642Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on comonotonic additivity

Published online by Cambridge University Press:  18 May 2009

June M. Parker
June M. Parker
Affiliation:
School of Mathematicsm University of Hull, Cottingham Road, Hull HU6 7Rx.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The axiom of comonotonic independence for a preference ordering was introduced by Schmeidler [9]. It leads to the comonotonic additivity for the functional representing the preference ordering, which is necessarily a Choquet integral.

The aim of this paper is to illuminate the concepts of comonotonicity, comonotonic independence and comonotonic additivity. For example the seemingly weaker condition of weak comonotonic independence used by Chateauneuf in [2] is seen to be equivalent to comonotonic independence. Comonotonic additivity is characterized as additivity on chains of sets. From this the characterization of Choquet integrals in [4], [1], [8] follows easily.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 38 , Issue 2 , May 1996 , pp. 199 - 205
Copyright
Copyright © Glasgow Mathematical Journal Trust 1996

References

1.Anger, B., Representation of capacities, Math. Ann. 229 (1977), 245–258.Google Scholar
2.Chateauneuf, A., On the use of capacities in modelling uncertainty aversion and risk aversion, J. Math. Economics 20 (1991), 343–369.CrossRefGoogle Scholar
3.Choquet, G., Theory of capacities, Ann. Inst. Fourier 5 (1953–1954), 131–295.CrossRefGoogle Scholar
4.Dellacherie, C., Quelques commentaires sur les prolongements de capacityés, Séminaire de Probabilités V, Strasbourg, Lecture Notes in Mathematics 191 (Springer-Verlag, 1970), 77–81.CrossRefGoogle Scholar
5.Denneberg, D., Non–additive Measure and Integral(Kluwer, 1994).Google Scholar
6.Gilboa, I., Schmeidler, D., Maxmin expected utility with non–unique prior, J. Math. Economics 18 (1989), 141–153.CrossRefGoogle Scholar
7.Greco, G.,Sur la mesurabilité d'une fonction numerique par rapport á une famille d'ensembles, Rend. Sem. Mat. Univ. Padova 65 (1981), 163–176.Google Scholar
8.Schmeidler, D., Integral representation without additivity, Proc. Amer. Math. Soc. 97 (1986), 255–261.CrossRefGoogle Scholar
9.Schmeidler, D., Subjective probability and expected utility without additivity, Econometrica 57 (1989), 571–587.CrossRefGoogle Scholar
10.Topsøe, F., On construction of measures, Proc. conference, Topology and Measure I, Zinnowitz, Ernst-Moritz-Arndt Univ., Greifswald, 1978, 343–381.Google Scholar