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Modeling attitudes towards uncertainty and risk through the use of choquet integral

  • Modeling Beliefs and Preferences
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Abstract

The aim of this paper is to present in a unified framework a survey of some results related to Choquet Expected Utility (CEU) models, a promising class of models introduced separately by Quiggin [35], Yaari [48] and Schmeidler [40, 41] which allow to separate attitudes towards uncertainty (or risk) from attitudes towards wealth, while respecting the first order stochastic dominance axiom.

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References

  1. M. Allais, Le comportement de l'homme rationnel devant le risque: Critique des postulats et axiomes de l'école américaine, Econometrica 21 (1953) 503–546.

    Google Scholar 

  2. M. Allais, The general theory of random choices in relation to the invariant cardinal utility function and the specific probability function, in:Risk, Decision and Rationality, ed. B. R. Munier (Reidel, Dordrecht, 1988) pp. 233–289.

    Google Scholar 

  3. T. E. Armstrong, Comonotonicity, simplicial subdivision of cubes and non-linear expected utility via Choquet integrals, Working Paper, University of Maryland, MD (1990).

    Google Scholar 

  4. A. Chateauneuf, On the use of comonotonicity in the axiomatization of EURDP theory for arbitrary consequences, presented atFUR V, Durham, Working Paper, CERMSEM, Paris (1990).

    Google Scholar 

  5. A. Chateauneuf, On the use of capacities in modeling uncertainty aversion and risk aversion. J. Math. Econ. 20 (1991) 343–369.

    Article  Google Scholar 

  6. A. Chateauneuf and M. Cohen, Risk seeking with diminishing marginal utility in a non-expected utility model, J. Risk and Uncertainty 9 (1994), to appear.

  7. A. Chateauneuf and J. Y. Jaffray, Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion, Math. Social Sci. 17 (1989) 263–283.

    Article  Google Scholar 

  8. A. Chateauneuf, R. Kast and A. Lapied, Pricing in slack markets, Working Paper, Université de Paris I, GREQE Marseille, Université de Toulon (1992).

  9. A. Chateauneuf, R. Kast and A. Lapied, Choquet pricing for financial markets with frictions, Working Paper, Université de Paris I, GREQE Marseille, Université de Toulon (1992).

  10. S. H. Chew, An axiomatic generalization of the quasilinear mean and Gini mean with application to decision theory (1989), rewritten version of S. H. Chew, An axiomatization of the rank-dependent quasilinear mean generalizing the Gini mean and the quasilinear mean, Economics Working Paper #156, Johns Hopkins University (1985).

  11. S. Chew and E. Karni, Choquet Expected Utility with finite state space: Commutativity and actindependence, (1992), J. Econ. Theory, to appear.

  12. S. Chew, E. Karni and Z. Safra, Risk aversion in the theory of expected utility with rank dependent preferences, J. Econ. Theory 42 (1987) 370–381.

    Article  Google Scholar 

  13. S. Chew and P. P. Wakker, Generalizing Choquet expected utility by weakening Savage's surething principle, Working Paper, University of California, University of Nijmegen (1991).

  14. G. Choquet, Théorie des capacités, Ann. Inst. Fourier (Grenoble) V (1953) 131–295.

    Google Scholar 

  15. C. Dellacherie, Quelques commentaires sur les prolongements de capacités,Séminaire de Probabilités V, Strasbourg, Lecture Notes in Mathematics, Vol. 191 (Springer, Berlin, 1970).

    Google Scholar 

  16. A. P. Dempster, Upper and lower probabilities induced by a multivalued mapping, Ann. Math. Statist. 38 (1967) 325–339.

    Google Scholar 

  17. D. Denneberg, Distorted probabilities and insurance premiums, Working Paper, University of Bremen (1990).

  18. D. Denneberg, Lectures on non-additive measure and integral, Preprint no. 42, University of Bremen (1992).

  19. J. Dow and S. Werlang, Uncertainty aversion, risk aversion, and the optimal choice of portfolio, Econometrica 60 (1992) 197–204.

    Google Scholar 

  20. R. Dyckherhoff and K. Mosler, Stochastic dominance with nonadditive probabilities, Zeits. Oper. Res. 37 (1993) 319–340.

    Google Scholar 

  21. D. Ellsberg, Risk, ambiguity and the Savage axioms, Quart. J. Econ. 75 (1961) 643–669.

    Google Scholar 

  22. L. G. Epstein, Behaviour under risk: Recent developments in theory and applications, Working Paper, University of Toronto (1990).

  23. L. G. Epstein and T. Wang, Intertemporal asset pricing under Knightian uncertainty, Econometrica 62 (1994) 283–322.

    Google Scholar 

  24. P. C. Fisburn,Nonlinear Preference and Utility Theory (The Johns Hopkins University Press, Baltimore, 1988).

    Google Scholar 

  25. I. Gilboa, Expected utility with purely subjective non-additive probabilities, J. Math. Econ. 16 (1987) 65–88.

    Article  Google Scholar 

  26. I. Gilboa and D. Schmeidler, Additive representations of non-additive measures and the Choquet integral, Working Paper, Northwestern University, Tel Aviv University (1992).

  27. I. Gilboa and D. Schmeidler, Canonical representation of set functions, Working Paper, Northwestern University, Tel Aviv University (1992).

  28. G. H. Greco, Sulla rappresentazione di funzionali mediante integrali, Rend. Sem. Mat. Univ. Padova 66 (1982) 21–42.

    Google Scholar 

  29. J. R. Green and B. Jullien, Ordinal independence in nonlinear utility theory, J. Risk and Uncertainty 1 (1988) 355–387.

    Article  Google Scholar 

  30. J. Y. Jaffray, Linear utility theory for belief functions, Oper. Res. Lett. 8 (1989) 107–112.

    Article  Google Scholar 

  31. P. Kischka and C. Puppe, Decisions under risk and uncertainty: A survey of recent developments, Zeits. Oper. Res. 36 (1992) 125–147.

    MathSciNet  Google Scholar 

  32. Y. Nakamura, Subjective expected utility with non-additive probabilities on finite state spaces, J. Econ. Theory 51 (1990) 346–366.

    Article  Google Scholar 

  33. Y. Nakamura, Rank dependent utility for arbitrary consequence spaces, Working Paper, University of Tsukuba (1991).

  34. Y. Nakamura, Multisymmetric structures and non-expected utility, J. Math. Psychol. 36 (1992) 375–395.

    Article  Google Scholar 

  35. J. Quiggin, A theory of anticipated utility, J. Econ. Behavior and Organization 3 (1982) 323–343.

    Article  Google Scholar 

  36. J. Quiggin and P. P. Wakker, The axiomatic basics of anticipated utility: A clarification, (1992), J. Econ. Theory, to appear.

  37. R. Sarin and P. P. Wakker, A simple axiomatization of nonadditive expected utility, Econometrica 60 (1992) 1255–1272.

    Google Scholar 

  38. L. J. Savage,The Foundations of Statistics (Wiley, New York, 1954; 2nd ed. Dover, New York, 1972).

    Google Scholar 

  39. M. Scarsini, Dominance conditions in non-additive expected utility theory, J. Math. Econ. 21 (1992) 173–184.

    Article  Google Scholar 

  40. D. Schmeidler, Integral representation without additivity, Proc. AMS 97 (1986) 255–261.

    Google Scholar 

  41. D. Schmeidler, Subjective probability and expected utility without additivity, Econometrica 57 (1989) 571–587; first version: Subjective expected utility without additivity, Foerder Institute Working Paper (1982).

    Google Scholar 

  42. U. Segal, Anticipated utility: A measure representation approach, Ann. Oper. Res. 19 (1989) 359–373.

    Google Scholar 

  43. U. Segal, The measure representation: A correction, J. Risk and Uncertainty 6 (1993) 99–107.

    Article  Google Scholar 

  44. G. Shafer,A Mathematical Theory of Evidence (Princeton University Press, Princeton, NJ, 1976).

    Google Scholar 

  45. L. S. Shapley, Cores of convex games, Int. J. Game Theory 1 (1971) 11–26.

    Article  Google Scholar 

  46. A. Tversky and D. Kahhneman, Advances in prospect theory: Cumulative representation of uncertainty, J. Risk and Uncertainty 5 (1992) 297–323.

    Article  Google Scholar 

  47. J. von Neumann and O. Morgenstern,Theory of Games and Economic Behavior (Princeton University Press, Princeton, NJ, 1947).

    Google Scholar 

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

    Google Scholar 

  49. M. Yaari, A controversial proposal concerning inequality measurement, J. Econ. Theory 44 (1988) 381–397.

    Article  Google Scholar 

  50. P. P. Wakker, Continuous subjective expected utility with non-additive probabilities. J. Math. Econ. 18 (1989) 1–27.

    Article  Google Scholar 

  51. P. P. Wakker,Additive Representations of Preferences (Kluwer, Dordrecht, 1989).

    Google Scholar 

  52. P. P. Wakker, Under stochastic dominance Choquet-expected utility and anticipated utility are identical, Theory and Decision 29 (1990) 119–132.

    Article  MathSciNet  Google Scholar 

  53. P. P. Wakker, Characterizing optimism and pessimism directly through comonotonicity, J. Econ. Theory 52 (1990) 453–463.

    Article  MathSciNet  Google Scholar 

  54. P.P. Wakker, Separating marginal utility and probabilistic risk aversion, Theory and Decision 36 (1994) 1–44.

    Article  Google Scholar 

  55. P. P. Wakker and A. Tversky, An axiomatization of cumulative prospect theory, J. Risk and Uncertainty 7 (1993) 147–176.

    Article  Google Scholar 

  56. J. A. Weymark, Generalized Gini inequality indices, Math. Social Sci. 1 (1981) 409–430.

    Article  Google Scholar 

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Chateauneuf, A. Modeling attitudes towards uncertainty and risk through the use of choquet integral. Ann Oper Res 52, 1–20 (1994). https://doi.org/10.1007/BF02032158

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