IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v62y2016icp75-89.html
   My bibliography  Save this article

Risk neutrality regions

Author

Listed:
  • Kannai, Yakar
  • Selden, Larry
  • Kang, Minwook
  • Wei, Xiao

Abstract

An Expected Utility maximizer can be risk neutral over a set of nondegenerate multivariate distributions even though her NM (von Neumann Morgenstern) index is not linear. We provide necessary and sufficient conditions for an individual with a concave NM utility to exhibit risk neutral behavior and characterize the regions of the choice space over which risk neutrality is exhibited. The least concave decomposition of the NM index introduced by Debreu (1976) plays an important role in our analysis as do the notions of minimum concavity points and minimum concavity directions. For the special case where one choice variable is certain, the analysis of risk neutrality requires modification of the Debreu decomposition. The existence of risk neutrality regions is shown to have important implications for the classic consumption–savings and representative agent equilibrium asset pricing models.

Suggested Citation

  • Kannai, Yakar & Selden, Larry & Kang, Minwook & Wei, Xiao, 2016. "Risk neutrality regions," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 75-89.
    • Handle: RePEc:eee:mateco:v:62:y:2016:i:c:p:75-89
    DOI: 10.1016/j.jmateco.2015.10.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406815001287
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2015.10.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Richard E. Kihlstrom & Leonard J. Mirman, 1981. "Constant, Increasing and Decreasing Risk Aversion with Many Commodities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(2), pages 271-280.
    2. Hellwig, Martin, 2004. "Risk Aversion in the Small and in the Large When Outcomes Are Multidimensional," Sonderforschungsbereich 504 Publications 04-22, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    3. Aumann, Robert J, 1975. "Values of Markets with a Continuum of Traders," Econometrica, Econometric Society, vol. 43(4), pages 611-646, July.
    4. Kihlstrom, Richard, 2009. "Risk aversion and the elasticity of substitution in general dynamic portfolio theory: Consistent planning by forward looking, expected utility maximizing investors," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 634-663, September.
    5. Scott F. Richard, 1975. "Multivariate Risk Aversion, Utility Independence and Separable Utility Functions," Management Science, INFORMS, vol. 22(1), pages 12-21, September.
    6. Deaton,Angus & Muellbauer,John, 1980. "Economics and Consumer Behavior," Cambridge Books, Cambridge University Press, number 9780521296762.
    7. Debreu, Gerard, 1976. "Least concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 121-129, July.
    8. Yakar Kannai & Larry Selden, 2014. "Violation of the Law of Demand," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(1), pages 1-28, January.
    9. Machina, Mark J, 2001. "Payoff Kinks in Preferences over Lotteries," Journal of Risk and Uncertainty, Springer, vol. 23(3), pages 207-260, November.
    10. Kihlstrom, Richard E. & Mirman, Leonard J., 1974. "Risk aversion with many commodities," Journal of Economic Theory, Elsevier, vol. 8(3), pages 361-388, July.
    11. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, Decembrie.
    12. Grant, Simon & Kajii, Atsushi & Polak, Ben, 1992. "Many good risks: An interpretation of multivariate risk and risk aversion without the Independence axiom," Journal of Economic Theory, Elsevier, vol. 56(2), pages 338-351, April.
    13. Duncan, George T, 1977. "A Matrix Measure of Multivariate Local Risk Aversion," Econometrica, Econometric Society, vol. 45(4), pages 895-903, May.
    14. Robert A. Pollak, 1971. "Additive Utility Functions and Linear Engel Curves," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(4), pages 401-414.
    15. Karni, Edi, 1979. "On Multivariate Risk Aversion," Econometrica, Econometric Society, vol. 47(6), pages 1391-1401, November.
    16. Rossman, Michael & Selden, Larry, 1978. "Time preferences, conditional risk preferences, and two-period cardinal utility," Journal of Economic Theory, Elsevier, vol. 19(1), pages 64-83, October.
    17. Larry Selden, 1979. "An OCE Analysis of the Effect of Uncertainty on Saving under Risk Preference Independence," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(1), pages 73-82.
    18. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sudhir A. Shah, 2016. "The Generalized Arrow-Pratt Coefficient," Working papers 254, Centre for Development Economics, Delhi School of Economics.
    2. Louis Eeckhoudt & Elisa Pagani & Eugenio Peluso, 2023. "Multidimensional risk aversion: the cardinal sin," Annals of Operations Research, Springer, vol. 320(1), pages 15-31, January.
    3. Steffen Andersen & James C. Cox & Glenn W. Harrison & Morten Lau & Elisabet E. Rutstroem & Vjollca Sadiraj, 2011. "Asset Integration and Attitudes to Risk: Theory and Evidence," Working Papers 2011_10, Durham University Business School.
    4. Yonatan Aumann, 2015. "A conceptual foundation for the theory of risk aversion," Discussion Paper Series dp686, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    5. Yakar Kannai & Larry Selden, 2014. "Violation of the Law of Demand," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(1), pages 1-28, January.
    6. Diego Nocetti & William T. Smith, 2011. "Precautionary Saving and Endogenous Labor Supply with and without Intertemporal Expected Utility," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43(7), pages 1475-1504, October.
    7. Ahmed, Mohamed M. & Preckel, Paul V. & Baker, Timothy G. & Lopez-Pereira, Miguel, 2001. "Modeling the impact of technological change on nutrition and marketed surplus," Agricultural Economics, Blackwell, vol. 25(1), pages 103-118, June.
    8. Elisa Pagani, 2015. "Certainty Equivalent: Many Meanings of a Mean," Working Papers 24/2015, University of Verona, Department of Economics.
    9. Ali E. Abbas, 2011. "Decomposing the Cross Derivatives of a Multiattribute Utility Function into Risk Attitude and Value," Decision Analysis, INFORMS, vol. 8(2), pages 103-116, June.
    10. Crainich, David & Eeckhoudt, Louis & Le Courtois, Olivier, 2017. "Health and portfolio choices: A diffidence approach," European Journal of Operational Research, Elsevier, vol. 259(1), pages 273-279.
    11. Sudhir A. Shah, 2009. "Duality Mappings For The Theory of Risk Aversion with Vector Outcomes," Working Papers id:2085, eSocialSciences.
    12. Antoine Bommier & François Le Grand, 2019. "Risk Aversion and Precautionary Savings in Dynamic Settings," Management Science, INFORMS, vol. 65(3), pages 1386-1397, March.
    13. Nocetti Diego & Smith William T, 2010. "Uncertainty, the Demand for Health Care, and Precautionary Saving," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 10(1), pages 1-31, August.
    14. Oscar Lau C., 2019. "Disentangling Intertemporal Substitution and Risk Aversion Under the Expected Utility Theorem," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 19(2), pages 1-14, June.
    15. Smith, William & Son, Young Seob, 2005. "Can the desire to conserve our natural resources be self-defeating?," Journal of Environmental Economics and Management, Elsevier, vol. 49(1), pages 52-67, January.
    16. Sudhir A. Shah, 2010. "Comparative Risk Aversion When the Outcomes are Vectors," Working Papers id:2907, eSocialSciences.
    17. Nocetti, Diego & Smith, William T., 2011. "Price uncertainty, saving, and welfare," Journal of Economic Dynamics and Control, Elsevier, vol. 35(7), pages 1139-1149, July.
    18. Sudhir A. Shah, 2006. "Comparative risk aversion when the outcomes are vectors," Working papers 149, Centre for Development Economics, Delhi School of Economics.
    19. Robert Jarrow & Siguang Li, 2021. "Concavity, stochastic utility, and risk aversion," Finance and Stochastics, Springer, vol. 25(2), pages 311-330, April.
    20. Echazu Luciana & Nocetti Diego & Smith William T., 2012. "A New Look into the Determinants of the Ecological Discount Rate: Disentangling Social Preferences," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 12(1), pages 1-44, April.

    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:eee:mateco:v:62:y:2016:i:c:p:75-89. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.