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Arrow-Pratt Measures of Risk Aversion: The Multivariate Case

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  • Levy, Haim
  • Levy, Azriel

Abstract

Arrow-Pratt measures of risk aversion have been defined for the univariate case. For utility functions having the same ordinal preferences, the authors extend K. J. Arrow's probability premium index to the multivariate case and obtain a unique solution that can be employed to risk-aversion comparison analysis. They also extend G. T. Duncan's definition of the risk premium vector and show that it can be employed in comparative risk aversion once they confine themselves to the same preference ordering. Hence, the authors end up with two multivariate risk indexes that are parallel to the Arrow and Pratt univariate indexes. Copyright 1991 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Suggested Citation

  • Levy, Haim & Levy, Azriel, 1991. "Arrow-Pratt Measures of Risk Aversion: The Multivariate Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(4), pages 891-898, November.
    • Handle: RePEc:ier:iecrev:v:32:y:1991:i:4:p:891-98
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    Cited by:

    1. Sudhir A. Shah, 2009. "Duality Mappings For The Theory of Risk Aversion with Vector Outcomes," Working Papers id:2085, eSocialSciences.
    2. Sudhir A. Shah, 2016. "The Generalized Arrow-Pratt Coefficient," Working Papers id:10795, eSocialSciences.
    3. Juan Martínez-Legaz & John Quah, 2007. "A contribution to duality theory, applied to the measurement of risk aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(2), pages 337-362, February.
    4. Sudhir A. Shah, 2007. "Duality mappings for the theory of risk aversion with vector outcomes," Working papers 160, Centre for Development Economics, Delhi School of Economics.
    5. Sudhir A. Shah, 2016. "The Generalized Arrow-Pratt Coefficient," Working papers 254, Centre for Development Economics, Delhi School of Economics.
    6. Gregor Dorfleitner & Michael Krapp, 2007. "On multiattributive risk aversion: some clarifying results," Review of Managerial Science, Springer, vol. 1(1), pages 47-63, April.

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