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Local Utility and Multivariate Risk Aversion

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Author Info

  • Arthur Charpentier

    (D�partement de math�matiques, Universit� du Qu�bec � Montr�al)

  • Alfred Galichon

    (Economics Department, Ecole Polytechnique)

  • Marc Henry

    (Department of Economics, Universit� de Montr�al)

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.

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Bibliographic Info

Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-836.

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Length: 20 pages
Date of creation: Jan 2012
Date of revision:
Handle: RePEc:tky:fseres:2012cf836

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References

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  1. Zephyr, 2010. "The city," City, Taylor & Francis Journals, vol. 14(1-2), pages 154-155, February.
  2. 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.
  3. Machina, Mark J, 1982. "A Stronger Characterization of Declining Risk Aversion," Econometrica, Econometric Society, vol. 50(4), pages 1069-79, July.
  4. Puccetti, Giovanni & Scarsini, Marco, 2010. "Multivariate comonotonicity," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 291-304, January.
  5. Mark J Machina, 1982. ""Expected Utility" Analysis without the Independence Axiom," Levine's Working Paper Archive 7650, David K. Levine.
  6. Filippo Santambrogio & Guillaume Carlier & Alfred Galichon, 2010. "From Knothe's transport to Brenier's map and a continuation method for optimal transport," Sciences Po publications info:hdl:2441/5rkqqmvrn4t, Sciences Po.
  7. 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.
  8. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  9. Marco Scarsini, 1988. "Dominance Conditions for Multivariate Utility Functions," Management Science, INFORMS, vol. 34(4), pages 454-460, April.
  10. 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 321-34, May.
  11. Stiglitz, Joseph E, 1969. "Behavior Towards Risk with Many Commodities," Econometrica, Econometric Society, vol. 37(4), pages 660-67, October.
  12. repec:hal:journl:halshs-00212281 is not listed on IDEAS
  13. 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.
  14. 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.
  15. Uzi Segal, 1986. "Some Remarks on Quiggin's Anticipated Utility," UCLA Economics Working Papers 392, UCLA Department of Economics.
  16. Kihlstrom, Richard E. & Mirman, Leonard J., 1974. "Risk aversion with many commodities," Journal of Economic Theory, Elsevier, vol. 8(3), pages 361-388, July.
  17. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc4c7eg1p is not listed on IDEAS
  18. 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.
  19. 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.
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