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Dominance Conditions for Multivariate Utility Functions

Author

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  • Marco Scarsini

    () (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique, Dipartimento di Scienze Economiche e Aziendali - LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma])

Abstract

Stochastic dominance conditions are given for n-variate utility functions, when k-variate risk aversion is assumed for k = 1, 2, ..., n. These conditions are expressed through a comparison of distribution functions, as in the well-known univariate case, and through a comparison of random variables defined on the same probability space.

Suggested Citation

  • Marco Scarsini, 1988. "Dominance Conditions for Multivariate Utility Functions," Post-Print hal-00542237, HAL.
  • Handle: RePEc:hal:journl:hal-00542237
    DOI: 10.1287/mnsc.34.4.454
    Note: View the original document on HAL open archive server: https://hal-hec.archives-ouvertes.fr/hal-00542237
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    Cited by:

    1. Range, Troels Martin & Østerdal, Lars Peter, 2013. "Checking bivariate first order dominance," Discussion Papers of Business and Economics 9/2013, University of Southern Denmark, Department of Business and Economics.
    2. Dionne, Georges & Li, Jingyuan, 2014. "Comparative Ross risk aversion in the presence of mean dependent risks," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 128-135.
    3. Ilia Tsetlin & Robert L. Winkler, 2009. "Multiattribute Utility Satisfying a Preference for Combining Good with Bad," Management Science, INFORMS, vol. 55(12), pages 1942-1952, December.
    4. Ortega, Eva-María & Escudero, Laureano F., 2010. "On expected utility for financial insurance portfolios with stochastic dependencies," European Journal of Operational Research, Elsevier, vol. 200(1), pages 181-186, January.
    5. Marta_Cardin & Paola_Ferretti, 2004. "Some theory of bivariate risk attitude," Game Theory and Information 0411009, University Library of Munich, Germany.
    6. Abdelaziz, F. Ben & Lang, P. & Nadeau, R., 1995. "Distributional efficiency in multiobjective stochastic linear programming," European Journal of Operational Research, Elsevier, vol. 85(2), pages 399-415, September.
    7. Decancq, Koen, 2012. "Elementary multivariate rearrangements and stochastic dominance on a Fréchet class," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1450-1459.
    8. Georges Dionne & Jingyuan Li, 2012. "Comparative Ross Risk Aversion in the Presence of Quadrant Dependent Risks," Cahiers de recherche 1226, CIRPEE.
    9. Arthur Charpentier & Alfred Galichon & Marc Henry, 2016. "Local Utility and Multivariate Risk Aversion," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 466-476, May.
    10. Østerdal, Lars Peter, 2010. "The mass transfer approach to multivariate discrete first order stochastic dominance: Direct proof and implications," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1222-1228, November.
    11. Marco Scarsini & Moshe Shaked, 1990. "Some conditions for stochastic equality," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(5), pages 617-625, October.
    12. F. Ben Abdelaziz & P. Lang & R. Nadeau, 1999. "Dominance and Efficiency in Multicriteria Decision under Uncertainty," Theory and Decision, Springer, vol. 47(3), pages 191-211, December.
    13. Denuit, Michel & Lefevre, Claude & Mesfioui, M'hamed, 1999. "A class of bivariate stochastic orderings, with applications in actuarial sciences," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 31-50, March.

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