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Local Utility and Multivariate Risk Aversion

Author

Listed:
  • Arthur Charpentier

    (Département de mathématiques, Université du Québec à Montréal)

  • Alfred Galichon

    (Economics Department, Ecole Polytechnique)

  • Marc Henry

    (Department of Economics, Université de Montréal)

Abstract

We revisit Machina's local utility as a tool to analyze attitudes to multivariate risks. Using martingale embedding techniques, we show that for nonexpected utility maximizers choosing between multivariate prospects, aversion to multivariate mean preserving increases in risk is equivalent to the concavity of the local utility functions, thereby generalizing Machina's result in [18]. To analyze comparative risk attitudes within the multivariate extension of rank dependen t expected utility of [10], we extend Quiggin's monotone mean and utility preserving increases in risk and show that the useful characterization given in [17] still holds in the multivariate case.

Suggested Citation

  • Arthur Charpentier & Alfred Galichon & Marc Henry, 2012. "Local Utility and Multivariate Risk Aversion," CIRJE F-Series CIRJE-F-836, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2012cf836
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    References listed on IDEAS

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    1. Puccetti, Giovanni & Scarsini, Marco, 2010. "Multivariate comonotonicity," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 291-304, January.
    2. Chateauneuf, Alain & Cohen, Michele & Meilijson, Isaac, 2004. "Four notions of mean-preserving increase in risk, risk attitudes and applications to the rank-dependent expected utility model," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 547-571, August.
    3. Diamond, Peter A. & Stiglitz, Joseph E., 1974. "Increases in risk and in risk aversion," Journal of Economic Theory, Elsevier, vol. 8(3), pages 337-360, July.
    4. Kihlstrom, Richard E. & Mirman, Leonard J., 1974. "Risk aversion with many commodities," Journal of Economic Theory, Elsevier, vol. 8(3), pages 361-388, July.
    5. Segal, Uzi, 1987. "Some remarks on Quiggin's anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 8(1), pages 145-154, March.
    6. Grant, Simon & Kajii, Atsushi & Polak, Ben, 1992. "Many good choice Axioms: When can many-good lotteries be treated as money lotteries?," Journal of Economic Theory, Elsevier, vol. 56(2), pages 313-337, April.
    7. Guillaume Carlier & Alfred Galichon & Filippo Santambrogio, 2008. "From Knothe’s transport to Brenier’s map and a continuation method for optimal transport," Sciences Po publications info:hdl:2441/5s1c4521ab8, Sciences Po.
    8. Larry G. Epstein & Stephen M. Tanny, 1980. "Increasing Generalized Correlation: A Definition and Some Economic Consequences," Canadian Journal of Economics, Canadian Economics Association, vol. 13(1), pages 16-34, February.
    9. Joseph E. Stiglitz, 1969. "A Note on Behavior towards Risk with Many Commodities," Cowles Foundation Discussion Papers 262, Cowles Foundation for Research in Economics, Yale University.
    10. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
    11. Marco Scarsini, 1988. "Dominance Conditions for Multivariate Utility Functions," Management Science, INFORMS, vol. 34(4), pages 454-460, April.
    12. Machina, Mark J, 1982. "A Stronger Characterization of Declining Risk Aversion," Econometrica, Econometric Society, vol. 50(4), pages 1069-1079, July.
    13. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc4c7eg1p is not listed on IDEAS
    14. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    15. Karni, Edi, 1989. "Generalized Expected Utility Analysis of Multivariate Risk Aversion," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(2), pages 297-305, May.
    16. Zephyr, 2010. "The city," City, Taylor & Francis Journals, vol. 14(1-2), pages 154-155, February.
    17. Safra, Zvi & Segal, Uzi, 1993. "Dominance Axioms and Multivariate Nonexpected Utility Preferences," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(2), pages 321-334, May.
    18. Stiglitz, Joseph E, 1969. "Behavior Towards Risk with Many Commodities," Econometrica, Econometric Society, vol. 37(4), pages 660-667, October.
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    Cited by:

    1. Zaiwu Gong & Chao Xu & Francisco Chiclana & Xiaoxia Xu, 2017. "Consensus Measure with Multi-stage Fluctuation Utility Based on China’s Urban Demolition Negotiation," Group Decision and Negotiation, Springer, vol. 26(2), pages 379-407, March.

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