IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-03569250.html
   My bibliography  Save this paper

Local Utility and Risk Aversion

Author

Listed:
  • Alfred Galichon
  • Arthur Charpentier

    (UR - Université de Rennes)

  • Marc Henry

    (CIRANO - Centre interuniversitaire de recherche en analyse des organisations - UQAM - Université du Québec à Montréal = University of Québec in Montréal, CIREQ - Centre interuniversitaire de recherche en économie quantitative)

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 Machina (1982). To analyze comparative risk attitudes within the multivariate extension of rank dependent expected utility of Galichon and Henry (2011), we extend Quiggin's monotone mean and utility preserving increases in risk and show that the useful characterization given in Landsberger and Meilijson (1994) still holds in the multivariate case.

Suggested Citation

  • Alfred Galichon & Arthur Charpentier & Marc Henry, 2012. "Local Utility and Risk Aversion," Post-Print hal-03569250, HAL.
    • Handle: RePEc:hal:journl:hal-03569250
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-03569250
    as

    Download full text from publisher

    File URL: https://sciencespo.hal.science/hal-03569250/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Carlier, G. & Dana, R.-A. & Galichon, A., 2012. "Pareto efficiency for the concave order and multivariate comonotonicity," Journal of Economic Theory, Elsevier, vol. 147(1), pages 207-229.
    3. 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.
    4. Kihlstrom, Richard E. & Mirman, Leonard J., 1974. "Risk aversion with many commodities," Journal of Economic Theory, Elsevier, vol. 8(3), pages 361-388, July.
    5. repec:dau:papers:123456789/9713 is not listed on IDEAS
    6. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc0p00hch is not listed on IDEAS
    7. 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.
    8. Louis Eeckhoudt & Béatrice Rey & Harris Schlesinger, 2007. "A Good Sign for Multivariate Risk Taking," Management Science, INFORMS, vol. 53(1), pages 117-124, January.
    9. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc0p00hch is not listed on IDEAS
    10. Galichon, Alfred & Henry, Marc, 2012. "Dual theory of choice with multivariate risks," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1501-1516.
    11. 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.
    12. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4c7eg1p is not listed on IDEAS
    13. 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.
    14. 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.
    15. Marco Scarsini, 1988. "Dominance Conditions for Multivariate Utility Functions," Management Science, INFORMS, vol. 34(4), pages 454-460, April.
    16. Guillaume Carlier & Alfred Galichon & Filippo Santambrogio, 2010. "From Knothe's transport to Brenier's map and a continuation method for optimal transport," Post-Print hal-01023796, HAL.
    17. Machina, Mark J, 1982. "A Stronger Characterization of Declining Risk Aversion," Econometrica, Econometric Society, vol. 50(4), pages 1069-1079, July.
    18. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4c7eg1p is not listed on IDEAS
    19. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    20. 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.
    21. Giovagnoli, Alessandra & Wynn, H. P., 1995. "Multivariate dispersion orderings," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 325-332, March.
    22. 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.
    23. Stiglitz, Joseph E, 1969. "Behavior Towards Risk with Many Commodities," Econometrica, Econometric Society, vol. 37(4), pages 660-667, October.
    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. Arthur Charpentier & Alfred Galichon & Marc Henry, 2012. "Local Utility and Multivariate Risk Aversion," CIRJE F-Series CIRJE-F-836, CIRJE, Faculty of Economics, University of Tokyo.
    2. repec:hal:spmain:info:hdl:2441/63913pp1o99dr9nneabam7071k is not listed on IDEAS
    3. repec:spo:wpmain:info:hdl:2441/63913pp1o99dr9nneabam7071k is not listed on IDEAS
    4. Arthur Charpentier & Alfred Galichon & Marc Henry, 2016. "Local Utility and Multivariate Risk Aversion," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 466-476, May.
    5. 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.
    6. Karni, Edi & Schmeidler, David, 1990. "Utility Theory and Uncertainty," Foerder Institute for Economic Research Working Papers 275480, Tel-Aviv University > Foerder Institute for Economic Research.
    7. Christoph Heinzel, 2014. "Term structure of discount rates under multivariate s-ordered consumption growth," Working Papers SMART 14-01, INRAE UMR SMART.
    8. 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.
    9. Jean Baccelli & Georg Schollmeyer & Christoph Jansen, 2022. "Risk aversion over finite domains," Theory and Decision, Springer, vol. 93(2), pages 371-397, September.
    10. Mao, Tiantian & Hu, Taizhong, 2012. "Characterization of left-monotone risk aversion in the RDEU model," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 413-422.
    11. Jouini, Elyès & Napp, Clotilde & Nocetti, Diego, 2013. "On multivariate prudence," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1255-1267.
    12. Grant, Simon & Quiggin, John, 2005. "Increasing uncertainty: a definition," Mathematical Social Sciences, Elsevier, vol. 49(2), pages 117-141, March.
    13. Galichon, Alfred & Henry, Marc, 2012. "Dual theory of choice with multivariate risks," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1501-1516.
    14. Guy Kaplanski & Haim Levy, 2017. "Envy and Altruism: Contrasting Bivariate and Univariate Prospect Preferences," Scandinavian Journal of Economics, Wiley Blackwell, vol. 119(2), pages 457-483, April.
    15. Sudhir A. Shah, 2009. "Duality Mappings For The Theory of Risk Aversion with Vector Outcomes," Working Papers id:2085, eSocialSciences.
    16. Ghossoub, Mario & He, Xue Dong, 2021. "Comparative risk aversion in RDEU with applications to optimal underwriting of securities issuance," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 6-22.
    17. 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.
    18. Marta_Cardin & Paola_Ferretti, 2004. "Some theory of bivariate risk attitude," Game Theory and Information 0411009, University Library of Munich, Germany.
    19. Colson, Gérard, 1993. "Prenons-nous assez de risque dans les théories du risque?," L'Actualité Economique, Société Canadienne de Science Economique, vol. 69(1), pages 111-141, mars.
    20. Christian Gollier & James Hammitt & Nicolas Treich, 2013. "Risk and choice: A research saga," Journal of Risk and Uncertainty, Springer, vol. 47(2), pages 129-145, October.
    21. 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.
    22. Gollier, Christian, 2021. "A general theory of risk apportionment," Journal of Economic Theory, Elsevier, vol. 192(C).

    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:hal:journl:hal-03569250. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.