IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v49y2003i8p1089-1104.html
   My bibliography  Save this article

A Generalization of Pratt-Arrow Measure to Nonexpected-Utility Preferences and Inseparable Probability and Utility

Author

Listed:
  • Robert F. Nau

    () (Fuqua School of Business, Duke University, Durham, North Carolina 27708-0120)

Abstract

The Pratt-Arrow measure of local risk aversion is generalized for the n-dimensional state-preference model of choice under uncertainty in which the decision maker may have inseparable subjective probabilities and utilities, unobservable stochastic prior wealth, and/or smooth nonexpected-utility preferences. Local risk aversion is measured by the matrix of derivatives of the decision maker's risk-neutral probabilities, without reference to true subjective probabilities or riskless wealth positions, and comparative risk aversion is measured without requiring agreement on true probabilities. Risk-neutral probabilities and their derivatives are shown to be sufficient statistics for approximately optimal investment and financing decisions in complete markets for contingent claims.

Suggested Citation

  • Robert F. Nau, 2003. "A Generalization of Pratt-Arrow Measure to Nonexpected-Utility Preferences and Inseparable Probability and Utility," Management Science, INFORMS, vol. 49(8), pages 1089-1104, August.
  • Handle: RePEc:inm:ormnsc:v:49:y:2003:i:8:p:1089-1104
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.49.8.1089.16398
    Download Restriction: no

    References listed on IDEAS

    as
    1. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    2. Kelsey, David & Nordquist, Gerald L, 1991. "A More General Measure of Risk Aversion When Utility Is State-Dependent," Oxford Economic Papers, Oxford University Press, vol. 43(1), pages 59-74, January.
    3. Robert Nau, 2001. "De Finetti was Right: Probability Does Not Exist," Theory and Decision, Springer, vol. 51(2), pages 89-124, December.
    4. Schlee, Edward E & Schlesinger, Harris, 1993. "The Valuation of Contingent Claims Markets," Journal of Risk and Uncertainty, Springer, vol. 6(1), pages 19-31, January.
    5. Hong, Chew Soo & Karni, Edi & Safra, Zvi, 1987. "Risk aversion in the theory of expected utility with rank dependent probabilities," Journal of Economic Theory, Elsevier, vol. 42(2), pages 370-381, August.
    6. Edi Karni & Philippe Mongin, 2000. "On the Determination of Subjective Probability by Choices," Management Science, INFORMS, vol. 46(2), pages 233-248, February.
    7. James E. Smith & Robert F. Nau, 1995. "Valuing Risky Projects: Option Pricing Theory and Decision Analysis," Management Science, INFORMS, vol. 41(5), pages 795-816, May.
    8. J. Hirshleifer, 1965. "Investment Decision under Uncertainty: Choice—Theoretic Approaches," The Quarterly Journal of Economics, Oxford University Press, vol. 79(4), pages 509-536.
    9. Edi Karni, 1995. "Non-Expected Utility and The Robustness of the Classical Insurance Paradigm: Discussion," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 20(1), pages 51-56, June.
    10. Peter Fishburn & Peter Wakker, 1995. "The Invention of the Independence Condition for Preferences," Management Science, INFORMS, vol. 41(7), pages 1130-1144, July.
    11. Segal, Uzi & Spivak, Avia, 1990. "First order versus second order risk aversion," Journal of Economic Theory, Elsevier, vol. 51(1), pages 111-125, June.
    12. Karni, Edi, 1983. "Risk Aversion for State-Dependent Utility Functions: Measurement and Applications," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 637-647, October.
    13. Yaari, Menahem E., 1969. "Some remarks on measures of risk aversion and on their uses," Journal of Economic Theory, Elsevier, vol. 1(3), pages 315-329, October.
    14. Mark Rubinstein, 1976. "The Valuation of Uncertain Income Streams and the Pricing of Options," Bell Journal of Economics, The RAND Corporation, vol. 7(2), pages 407-425, Autumn.
    15. Pratt, John W, 1988. "Aversion to One Risk in the Presence of Others," Journal of Risk and Uncertainty, Springer, vol. 1(4), pages 395-413, December.
    16. Courtault, Jean-Michel & Gayant, Jean-Pascal, 1998. "Local risk aversion in the rank dependent expected utility model: First order versus second order effects," Economics Letters, Elsevier, vol. 59(2), pages 207-212, May.
    17. Larry G. Epstein, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Oxford University Press, vol. 66(3), pages 579-608.
    18. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    19. Ross, Stephen A, 1978. "A Simple Approach to the Valuation of Risky Streams," The Journal of Business, University of Chicago Press, vol. 51(3), pages 453-475, July.
    20. Eeckhoudt, Louis & Gollier, Christian & Schlesinger, Harris, 1996. "Changes in Background Risk and Risk-Taking Behavior," Econometrica, Econometric Society, vol. 64(3), pages 683-689, May.
    21. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
    22. Ross, Stephen A, 1981. "Some Stronger Measures of Risk Aversion in the Small and the Large with Applications," Econometrica, Econometric Society, vol. 49(3), pages 621-638, May.
    23. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    24. K. J. Arrow, 1964. "The Role of Securities in the Optimal Allocation of Risk-bearing," Review of Economic Studies, Oxford University Press, vol. 31(2), pages 91-96.
    25. Kihlstrom, Richard E & Romer, David & Williams, Steve, 1981. "Risk Aversion with Random Initial Wealth," Econometrica, Econometric Society, vol. 49(4), pages 911-920, June.
    26. Nau, Robert F, 1995. "Coherent Decision Analysis with Inseparable Probabilities and Utilities," Journal of Risk and Uncertainty, Springer, vol. 10(1), pages 71-91, January.
    27. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-1123, September.
    28. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    29. Karni, Edi & Schmeidler, David & Vind, Karl, 1983. "On State Dependent Preferences and Subjective Probabilities," Econometrica, Econometric Society, vol. 51(4), pages 1021-1031, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hurley, Terrance M., 2016. "Slutsky, Let Me Introduce You to Arrow-Pratt: Competitive Price Effects with Uncertain Production," Staff Papers 250204, University of Minnesota, Department of Applied Economics.
    2. Robert Nau, 2015. "Risk-neutral equilibria of noncooperative games," Theory and Decision, Springer, vol. 78(2), pages 171-188, February.
    3. Louis R. Eeckhoudt & Roger J. A. Laeven, 2016. "Dual Moments and Risk Attitudes," Papers 1612.03347, arXiv.org, revised Mar 2018.
    4. André, Eric, 2014. "Optimal portfolio with vector expected utility," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 50-62.
    5. repec:pal:jorsoc:v:57:y:2006:i:3:d:10.1057_palgrave.jors.2601982 is not listed on IDEAS
    6. Elisa Pagani, 2015. "Certainty Equivalent: Many Meanings of a Mean," Working Papers 24/2015, University of Verona, Department of Economics.
    7. Costis Skiadas, 2015. "Dynamic choice with constant source-dependent relative risk aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(3), pages 393-422, November.
    8. repec:kap:theord:v:83:y:2017:i:1:d:10.1007_s11238-016-9584-6 is not listed on IDEAS

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:49:y:2003:i:8:p:1089-1104. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Matthew Walls). General contact details of provider: http://edirc.repec.org/data/inforea.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.