IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v75y2012i2p481-489.html
   My bibliography  Save this article

Relative concave utility for risk and ambiguity

Author

Listed:
  • Baillon, Aurélien
  • Driesen, Bram
  • Wakker, Peter P.

Abstract

This paper presents a general technique for comparing the concavity of different utility functions when probabilities need not be known. It generalizes: (a) Yaariʼs comparisons of risk aversion by not requiring identical beliefs; (b) Kreps and Porteusʼ information-timing preference by not requiring known probabilities; (c) Klibanoff, Marinacci, and Mukerjiʼs smooth ambiguity aversion by not using subjective probabilities (which are not directly observable) and by not committing to (violations of) dynamic decision principles; (d) comparative smooth ambiguity aversion by not requiring identical second-order subjective probabilities. Our technique completely isolates the empirical meaning of utility. It thus sheds new light on the descriptive appropriateness of utility to model risk and ambiguity attitudes.

Suggested Citation

  • Baillon, Aurélien & Driesen, Bram & Wakker, Peter P., 2012. "Relative concave utility for risk and ambiguity," Games and Economic Behavior, Elsevier, vol. 75(2), pages 481-489.
    • Handle: RePEc:eee:gamebe:v:75:y:2012:i:2:p:481-489
    DOI: 10.1016/j.geb.2012.01.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825612000097
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2012.01.006?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. 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.
    2. Yoram Halevy & Emre Ozdenoren, 2022. "Uncertainty and compound lotteries: calibration," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(2), pages 373-395, September.
    3. Tomasz Strzalecki, 2011. "Axiomatic Foundations of Multiplier Preferences," Econometrica, Econometric Society, vol. 79(1), pages 47-73, January.
    4. Charles M. Harvey, 1986. "Value Functions for Infinite-Period Planning," Management Science, INFORMS, vol. 32(9), pages 1123-1139, September.
    5. David M. Kreps & Evan L. Porteus, 2013. "Temporal von Neumann—Morgenstern and Induced Preferences," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 11, pages 181-206, World Scientific Publishing Co. Pte. Ltd..
    6. Larry G. Epstein, 2010. "A Paradox for the “Smooth Ambiguity” Model of Preference," Econometrica, Econometric Society, vol. 78(6), pages 2085-2099, November.
    7. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.
    8. Hans-Martin von Gaudecker & Arthur van Soest & Erik Wengstrom, 2011. "Heterogeneity in Risky Choice Behavior in a Broad Population," American Economic Review, American Economic Association, vol. 101(2), pages 664-694, April.
    9. 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..
    10. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
    11. Mohammed Abdellaoui & Han Bleichrodt & Corina Paraschiv, 2007. "Loss Aversion Under Prospect Theory: A Parameter-Free Measurement," Management Science, INFORMS, vol. 53(10), pages 1659-1674, October.
    12. Jean-Marc Tallon & Alain Chateauneuf, 2002. "Diversification, convex preferences and non-empty core in the Choquet expected utility model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(3), pages 509-523.
    13. Jean-Marc Tallon & Alain Chateauneuf, 2002. "Diversification, convex preferences and non-empty core in the Choquet expected utility model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(3), pages 509-523.
    14. Hans-Martin von Gaudecker & Arthur van Soest & Erik Wengstrom, 2011. "Heterogeneity in Risky Choice Behavior in a Broad Population," American Economic Review, American Economic Association, vol. 101(2), pages 664-694, April.
    15. William Neilson, 2010. "A simplified axiomatic approach to ambiguity aversion," Journal of Risk and Uncertainty, Springer, vol. 41(2), pages 113-124, October.
    16. Peter Klibanoff & Emre Ozdenoren, 2007. "Subjective recursive expected utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(1), pages 49-87, January.
    17. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    18. Yoram Halevy, 2007. "Ellsberg Revisited: An Experimental Study," Econometrica, Econometric Society, vol. 75(2), pages 503-536, March.
    19. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    20. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-1668, December.
    21. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2003. "A Subjective Spin on Roulette Wheels," Econometrica, Econometric Society, vol. 71(6), pages 1897-1908, November.
    22. Veronika Köbberling & Peter P. Wakker, 2003. "Preference Foundations for Nonexpected Utility: A Generalized and Simplified Technique," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 395-423, August.
    23. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    24. repec:bla:econom:v:58:y:1991:i:232:p:417-40 is not listed on IDEAS
    25. 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.
    26. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    27. Peter Fishburn & Ward Edwards, 1997. "Discount-neutral utility models for denumerable time streams," Theory and Decision, Springer, vol. 43(2), pages 139-166, September.
    28. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    29. Schoemaker, Paul J H, 1982. "The Expected Utility Model: Its Variants, Purposes, Evidence and Limitations," Journal of Economic Literature, American Economic Association, vol. 20(2), pages 529-563, June.
    30. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    31. Ergin, Haluk & Gul, Faruk, 2009. "A theory of subjective compound lotteries," Journal of Economic Theory, Elsevier, vol. 144(3), pages 899-929, May.
    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. Berger, Loïc & Bleichrodt, Han & Eeckhoudt, Louis, 2013. "Treatment decisions under ambiguity," Journal of Health Economics, Elsevier, vol. 32(3), pages 559-569.
    2. Larry G. Epstein & Martin Schneider, 2010. "Ambiguity and Asset Markets," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 315-346, December.
    3. Mohammed Abdellaoui & Ahmed Driouchi & Olivier L’Haridon, 2011. "Risk aversion elicitation: reconciling tractability and bias minimization," Theory and Decision, Springer, vol. 71(1), pages 63-80, July.
    4. Jinrui Pan & Craig Webb & Horst Zank, 2013. "Discounting the Subjective Present and Future," Economics Discussion Paper Series 1305, Economics, The University of Manchester.
    5. Aurélien Baillon & Olivier L’Haridon, 2021. "Discrete Arrow–Pratt indexes for risk and uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(4), pages 1375-1393, November.
    6. Christoph Bühren & Fabian Meier & Marco Pleßner, 2023. "Ambiguity aversion: bibliometric analysis and literature review of the last 60 years," Management Review Quarterly, Springer, vol. 73(2), pages 495-525, June.
    7. Katarzyna M. Werner & Horst Zank, 2019. "A revealed reference point for prospect theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(4), pages 731-773, June.
    8. 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.
    9. Wakker, Peter P. & Yang, Jingni, 2019. "A powerful tool for analyzing concave/convex utility and weighting functions," Journal of Economic Theory, Elsevier, vol. 181(C), pages 143-159.
    10. Xiangyu Qu, 2015. "A belief-based definition of ambiguity aversion," Theory and Decision, Springer, vol. 79(1), pages 15-30, July.
    11. Ulrich Schmidt & Horst Zank, 2012. "A genuine foundation for prospect theory," Journal of Risk and Uncertainty, Springer, vol. 45(2), pages 97-113, October.
    12. Mohammed Abdellaoui & Enrico Diecidue & Emmanuel Kemel & Ayse Onculer, 2021. "Temporal Risk Resolution: Utility versus Probability Weighting Approaches," Working Papers hal-03330225, HAL.
    13. Craig Webb, 2010. "Agreeing to spin the subjective roulette wheel: Bargaining with subjective mixtures," Economics Discussion Paper Series 1005, Economics, The University of Manchester.
    14. Katarzyna Werner & Horst Zank, 2012. "Foundations for Prospect Theory Through Probability Midpoint Consistency," Economics Discussion Paper Series 1210, Economics, The University of Manchester.
    15. Pan, Jinrui & Webb, Craig S. & Zank, Horst, 2015. "An extension of quasi-hyperbolic discounting to continuous time," Games and Economic Behavior, Elsevier, vol. 89(C), pages 43-55.
    16. Vieider, Ferdinand M. & Cingl, Lubomír & Martinsson, Peter & Stojic, Hrvoje, 2013. "Separating attitudes towards money from attitudes towards probabilities: Stake effects and ambiguity as a test for prospect theory," Discussion Papers, WZB Junior Research Group Risk and Development SP II 2013-401, WZB Berlin Social Science Center.
    17. Aurélien Baillon & Ning Liu & Dennie Dolder, 2017. "Comparing uncertainty aversion towards different sources," Theory and Decision, Springer, vol. 83(1), pages 1-18, June.

    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. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Wakker, Peter P. & Yang, Jingni, 2019. "A powerful tool for analyzing concave/convex utility and weighting functions," Journal of Economic Theory, Elsevier, vol. 181(C), pages 143-159.
    3. Izhakian, Yehuda, 2017. "Expected utility with uncertain probabilities theory," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 91-103.
    4. Stefan Trautmann & Peter P. Wakker, 2018. "Making the Anscombe-Aumann approach to ambiguity suitable for descriptive applications," Journal of Risk and Uncertainty, Springer, vol. 56(1), pages 83-116, February.
    5. Fan Wang, 2022. "Rank-Dependent Utility Under Multiple Priors," Management Science, INFORMS, vol. 68(11), pages 8166-8183, November.
    6. 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.
    7. Amit Kothiyal & Vitalie Spinu & Peter Wakker, 2014. "An experimental test of prospect theory for predicting choice under ambiguity," Journal of Risk and Uncertainty, Springer, vol. 48(1), pages 1-17, February.
    8. Gijs van de Kuilen & Peter P. Wakker, 2011. "The Midweight Method to Measure Attitudes Toward Risk and Ambiguity," Management Science, INFORMS, vol. 57(3), pages 582-598, March.
    9. Aurélien Baillon & Ning Liu & Dennie Dolder, 2017. "Comparing uncertainty aversion towards different sources," Theory and Decision, Springer, vol. 83(1), pages 1-18, June.
    10. Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Levine's Working Paper Archive 7616, David K. Levine.
    11. Han Bleichrodt & Jurgen Eichberger & Simon Grant & David Kelsey & Chen Li, 2018. "A Test of Dynamic Consistency and Consequentialism in the Presence of Ambiguity," Discussion Papers 1803, University of Exeter, Department of Economics.
    12. Laurent Denant-Boemont & Olivier L’Haridon, 2013. "La rationalité à l'épreuve de l'économie comportementale," Revue française d'économie, Presses de Sciences-Po, vol. 0(2), pages 35-89.
    13. Arthur E. Attema & Han Bleichrodt & Olivier L'Haridon, 2018. "Ambiguity preferences for health," Health Economics, John Wiley & Sons, Ltd., vol. 27(11), pages 1699-1716, November.
    14. Johanna Etner & Meglena Jeleva & Jean-Marc Tallon, 2009. "Decision theory under uncertainty," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00429573, HAL.
    15. Li, Jian, 2020. "Preferences for partial information and ambiguity," Theoretical Economics, Econometric Society, vol. 15(3), July.
    16. Norio Takeoka & Takashi Ui, 2021. "Imprecise Information and Second-Order Beliefs," Working Papers on Central Bank Communication 037, University of Tokyo, Graduate School of Economics.
    17. Jewitt, Ian & Mukerji, Sujoy, 2017. "Ordering ambiguous acts," Journal of Economic Theory, Elsevier, vol. 171(C), pages 213-267.
    18. Hui Chen & Nengjiu Ju & Jianjun Miao, 2014. "Dynamic Asset Allocation with Ambiguous Return Predictability," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(4), pages 799-823, October.
    19. Xiangyu Qu, 2015. "A belief-based definition of ambiguity aversion," Theory and Decision, Springer, vol. 79(1), pages 15-30, July.
    20. Evren, Özgür, 2019. "Recursive non-expected utility: Connecting ambiguity attitudes to risk preferences and the level of ambiguity," Games and Economic Behavior, Elsevier, vol. 114(C), pages 285-307.

    More about this item

    Keywords

    More risk averse; More ambiguity averse; Knightian uncertainty; Subjective probability; Nonexpected utility;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    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:eee:gamebe:v:75:y:2012:i:2:p:481-489. 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/inca/622836 .

    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.