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Local Utility and Multivariate Risk Aversion

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  • Arthur Charpentier
  • Alfred Galichon
  • Marc Henry

    ()

Abstract

We revisit Machina's local utility as a tool to analyze attitudes to multivariate risks. Using martingale embedding techniques, we show that for non-expected 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 dependent 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 CIRANO in its series CIRANO Working Papers with number 2012s-17.

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Date of creation: 01 Jun 2012
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Handle: RePEc:cir:cirwor:2012s-17

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Keywords: local utility; multivariate risk aversion; multivariate rank dependent utility; pessimism; multivariate Bickel-Lehmann dispersion;

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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. Alain Chateauneuf & Michèle Cohen & Isaac Meilijson, 2004. "Four notions of mean preserving increase in risk, risk attitudes and applications to the Rank-Dependent Expected Utility model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00212281, HAL.
  3. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
  4. Uzi Segal, 1986. "Some Remarks on Quiggin's Anticipated Utility," UCLA Economics Working Papers 392, UCLA Department of Economics.
  5. Marco Scarsini, 1988. "Dominance Conditions for Multivariate Utility Functions," Management Science, INFORMS, vol. 34(4), pages 454-460, April.
  6. 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.
  7. 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.
  8. Kihlstrom, Richard E. & Mirman, Leonard J., 1974. "Risk aversion with many commodities," Journal of Economic Theory, Elsevier, vol. 8(3), pages 361-388, July.
  9. 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.
  10. 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.
  11. Stiglitz, Joseph E, 1969. "Behavior Towards Risk with Many Commodities," Econometrica, Econometric Society, vol. 37(4), pages 660-67, October.
  12. Machina, Mark J, 1982. "A Stronger Characterization of Declining Risk Aversion," Econometrica, Econometric Society, vol. 50(4), pages 1069-79, July.
  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.
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