IDEAS home Printed from https://ideas.repec.org/a/wly/riskan/v32y2012i8p1277-1292.html
   My bibliography  Save this article

Mean‐Deviation Analysis in the Theory of Choice

Author

Listed:
  • Bogdan Grechuk
  • Anton Molyboha
  • Michael Zabarankin

Abstract

Mean‐deviation analysis, along with the existing theories of coherent risk measures and dual utility, is examined in the context of the theory of choice under uncertainty, which studies rational preference relations for random outcomes based on different sets of axioms such as transitivity, monotonicity, continuity, etc. An axiomatic foundation of the theory of coherent risk measures is obtained as a relaxation of the axioms of the dual utility theory, and a further relaxation of the axioms are shown to lead to the mean‐deviation analysis. Paradoxes arising from the sets of axioms corresponding to these theories and their possible resolutions are discussed, and application of the mean‐deviation analysis to optimal risk sharing and portfolio selection in the context of rational choice is considered.

Suggested Citation

  • Bogdan Grechuk & Anton Molyboha & Michael Zabarankin, 2012. "Mean‐Deviation Analysis in the Theory of Choice," Risk Analysis, John Wiley & Sons, vol. 32(8), pages 1277-1292, August.
    • Handle: RePEc:wly:riskan:v:32:y:2012:i:8:p:1277-1292
    DOI: 10.1111/j.1539-6924.2011.01611.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1539-6924.2011.01611.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1539-6924.2011.01611.x?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
    ---><---

    References listed on IDEAS

    as
    1. R. Rockafellar & Stan Uryasev & Michael Zabarankin, 2006. "Generalized deviations in risk analysis," Finance and Stochastics, Springer, vol. 10(1), pages 51-74, January.
    2. PAVLO A. Krokhmal, 2007. "Higher moment coherent risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 373-387.
    3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    4. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Montrucchio, L., 2011. "Uncertainty averse preferences," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1275-1330, July.
    5. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    6. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
    7. Bogdan Grechuk & Anton Molyboha & Michael Zabarankin, 2009. "Maximum Entropy Principle with General Deviation Measures," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 445-467, May.
    8. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    9. J. C. R. Alcantud & G. Bosi, 2003. "On the existence of certainty equivalents of various relevant types," Journal of Applied Mathematics, Hindawi, vol. 2003, pages 1-12, January.
    10. Safra, Zvi & Segal, Uzi, 1998. "Constant Risk Aversion," Journal of Economic Theory, Elsevier, vol. 83(1), pages 19-42, November.
    11. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    12. Bauerle, Nicole & Muller, Alfred, 2006. "Stochastic orders and risk measures: Consistency and bounds," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 132-148, February.
    13. Rockafellar, R. Tyrrell & Uryasev, Stan & Zabarankin, Michael, 2006. "Master funds in portfolio analysis with general deviation measures," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 743-778, February.
    14. R. Tyrrell Rockafellar & Stan Uryasev & Michael Zabarankin, 2008. "Risk Tuning with Generalized Linear Regression," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 712-729, August.
    15. Machina, Mark J, 1987. "Choice under Uncertainty: Problems Solved and Unsolved," Journal of Economic Perspectives, American Economic Association, vol. 1(1), pages 121-154, Summer.
    16. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    17. Rockafellar, R. Tyrrell & Uryasev, Stan & Zabarankin, M., 2007. "Equilibrium with investors using a diversity of deviation measures," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3251-3268, November.
    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. Angelini, Pierpaolo & Maturo, Fabrizio, 2022. "The price of risk based on multilinear measures," International Review of Economics & Finance, Elsevier, vol. 81(C), pages 39-57.
    2. Benati, S. & Conde, E., 2022. "A relative robust approach on expected returns with bounded CVaR for portfolio selection," European Journal of Operational Research, Elsevier, vol. 296(1), pages 332-352.
    3. Xia Han & Ruodu Wang & Qinyu Wu, 2023. "Monotonic mean-deviation risk measures," Papers 2312.01034, arXiv.org, revised Aug 2024.

    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. Grechuk, Bogdan & Zabarankin, Michael, 2014. "Inverse portfolio problem with mean-deviation model," European Journal of Operational Research, Elsevier, vol. 234(2), pages 481-490.
    2. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2012. "Probabilistic sophistication, second order stochastic dominance and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 271-283.
    3. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.
    4. Mohammed Abdellaoui & Horst Zank, 2023. "Source and rank-dependent utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 949-981, May.
    5. Zvi Safra & Uzi Segal, 2005. "Are Universal Preferences Possible? Calibration Results for Non-Expected Utility Theories," Boston College Working Papers in Economics 633, Boston College Department of Economics.
    6. Furman, Edward & Wang, Ruodu & Zitikis, Ričardas, 2017. "Gini-type measures of risk and variability: Gini shortfall, capital allocations, and heavy-tailed risks," Journal of Banking & Finance, Elsevier, vol. 83(C), pages 70-84.
    7. Gilles Boevi Koumou & Georges Dionne, 2022. "Coherent Diversification Measures in Portfolio Theory: An Axiomatic Foundation," Risks, MDPI, vol. 10(11), pages 1-19, October.
    8. Dean, Mark & Ortoleva, Pietro, 2017. "Allais, Ellsberg, and preferences for hedging," Theoretical Economics, Econometric Society, vol. 12(1), January.
    9. Marc Willinger, 1990. "La rénovation des fondements de l'utilité et du risque," Revue Économique, Programme National Persée, vol. 41(1), pages 5-48.
    10. Freeman, David, 2015. "Calibration without reduction for non-expected utility," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 21-32.
    11. Xia Han & Ruodu Wang & Xun Yu Zhou, 2022. "Choquet regularization for reinforcement learning," Papers 2208.08497, arXiv.org.
    12. Bogdan Grechuk & Michael Zabarankin, 2012. "Optimal risk sharing with general deviation measures," Annals of Operations Research, Springer, vol. 200(1), pages 9-21, November.
    13. Enrico G. De Giorgi & Ola Mahmoud, 2016. "Diversification preferences in the theory of choice," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(2), pages 143-174, November.
    14. Cillo, Alessandra & Delquié, Philippe, 2014. "Mean-risk analysis with enhanced behavioral content," European Journal of Operational Research, Elsevier, vol. 239(3), pages 764-775.
    15. Nielsen, Thomas D. & Jaffray, Jean-Yves, 2006. "Dynamic decision making without expected utility: An operational approach," European Journal of Operational Research, Elsevier, vol. 169(1), pages 226-246, February.
    16. Phillips Peter J. & Pohl Gabriela, 2018. "The Deferral of Attacks: SP/A Theory as a Model of Terrorist Choice when Losses Are Inevitable," Open Economics, De Gruyter, vol. 1(1), pages 71-85, February.
    17. Mickael Beaud & Marc Willinger, 2015. "Are People Risk Vulnerable?," Management Science, INFORMS, vol. 61(3), pages 624-636, March.
    18. Grechuk, Bogdan & Zabarankin, Michael, 2016. "Inverse portfolio problem with coherent risk measures," European Journal of Operational Research, Elsevier, vol. 249(2), pages 740-750.
    19. Fabio Maccheroni & Massimo Marinacci & Ruodu Wang & Qinyu Wu, 2023. "Risk Aversion and Insurance Propensity," Papers 2310.09173, arXiv.org, revised Jul 2024.
    20. Foster, Gigi & Frijters, Paul & Schaffner, Markus & Torgler, Benno, 2018. "Expectation formation in an evolving game of uncertainty: New experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 154(C), pages 379-405.

    More about this item

    Statistics

    Access and download statistics

    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:wly:riskan:v:32:y:2012:i:8:p:1277-1292. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1111/(ISSN)1539-6924 .

    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.