IDEAS home Printed from https://ideas.repec.org/p/icr/wpmath/18-2003.html
   My bibliography  Save this paper

Decision Making with Imprecise Probabilistic Information

Author

Listed:
  • Thibault Gajdos
  • Jean-Marc Tallon
  • Jean-Christophe Vergnaud

Abstract

We develop an axiomatic approach to decision under uncertainty that explicitly takes into account the information available to the decision maker. The information is described by a set of priors and a reference prior. We define a notion of imprecision for this informational setting and show that a decision maker who is averse to information imprecision maximizes the minimum expected utility computed with respect to a subset of the set of initially given priors. The extent to which this set is reduced can be seen as a measure of imprecision aversion. This approach thus allows a lot of flexibility in modelling the decision maker attitude towards imprecision. In contrast, applying Gilboa and Schmeidler (1989) maxmin criterion to the initial set of priors amounts to assuming extreme pessimism.

Suggested Citation

  • Thibault Gajdos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2002. "Decision Making with Imprecise Probabilistic Information," ICER Working Papers - Applied Mathematics Series 18-2003, ICER - International Centre for Economic Research, revised May 2003.
  • Handle: RePEc:icr:wpmath:18-2003
    as

    Download full text from publisher

    File URL: http://www.bemservizi.unito.it/repec/icr/wp2003/Gajdos18-03.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Massimo Marinacci & Luigi Montrucchio, 2003. "Cores and stable sets of finite dimensional games," ICER Working Papers - Applied Mathematics Series 07-2003, ICER - International Centre for Economic Research.
    2. Montrucchio, Luigi & Privileggi, Fabio, 2001. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," Journal of Economic Theory, Elsevier, vol. 101(1), pages 158-188, November.
    3. Gajdos, Thibault & Maurin, Eric, 2004. "Unequal uncertainties and uncertain inequalities: an axiomatic approach," Journal of Economic Theory, Elsevier, vol. 116(1), pages 93-118, May.
    4. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    5. Cohen, Michele & Jaffray, Jean-Yves, 1980. "Rational Behavior under Complete Ignorance," Econometrica, Econometric Society, vol. 48(5), pages 1281-1299, July.
    6. Thibault Gajdos & John Weymark, 2005. "Multidimensional generalized Gini indices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(3), pages 471-496, October.
    7. Segal, Uzi, 1987. "The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(1), pages 175-202, February.
    8. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
    9. Gajdos, Thibault & Tallon, Jean-Marc & Vergnaud, Jean-Christophe, 2004. "Decision making with imprecise probabilistic information," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 647-681, September.
    10. Erio Castagnoli & Fabio Maccheroni & Massimo Marinacci, 2004. "Choquet Insurance Pricing: A Caveat," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 481-485, July.
    11. Adriana Castaldo & Massimo Marinacci, 2001. "Random correspndences as bundles of random variables," ICER Working Papers - Applied Mathematics Series 12-2001, ICER - International Centre for Economic Research.
    12. Tapking, Jens, 2004. "Axioms for preferences revealing subjective uncertainty and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 771-797, November.
    13. Marinacci, Massimo & Montrucchio, Luigi, 2004. "A characterization of the core of convex games through Gateaux derivatives," Journal of Economic Theory, Elsevier, vol. 116(2), pages 229-248, June.
    14. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2005. "Certainty Independence and the Separation of Utility and Beliefs," Journal of Economic Theory, Elsevier, vol. 120(1), pages 129-136, January.
    15. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
    16. Umberto Cherubini & Elisa Luciano, 2002. "Multivariate Option Pricing with Copulas," ICER Working Papers - Applied Mathematics Series 05-2002, ICER - International Centre for Economic Research.
    17. Fabio Maccheroni, 2004. "Yaari's dual theory without the completeness axiom," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(3), pages 701-714, March.
    18. Castagnoli, Erio & Maccheroni, Fabio & Marinacci, Massimo, 2002. "Insurance premia consistent with the market," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 267-284, October.
    19. Maitreesh Ghatak & Massimo Morelli & Tomas Sjoström, 2001. "Credit rationing, wealth inequality, and allocation of talent," ICER Working Papers - Applied Mathematics Series 23-2001, ICER - International Centre for Economic Research.
    20. Domenico Menicucci, 2003. "Optimal two-object auctions with synergies," Review of Economic Design, Springer;Society for Economic Design, vol. 8(2), pages 143-164, October.
    21. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    22. 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.
    23. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci, 2002. "Ambiguity from the Differential Viewpoint," ICER Working Papers - Applied Mathematics Series 17-2002, ICER - International Centre for Economic Research.
    24. Larry G. Epstein, 1999. "A Definition of Uncertainty Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 579-608.
    25. Steven Haberman & Elena Vigna, 2002. "Optimal investment strategies and risk measures in defined contribution pension schemes," ICER Working Papers - Applied Mathematics Series 09-2002, ICER - International Centre for Economic Research.
    26. 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.
    27. Haberman, Steven & Vigna, Elena, 2002. "Optimal investment strategies and risk measures in defined contribution pension schemes," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 35-69, August.
    28. 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.
    29. Renault, Jerome & Scarlatti, Sergio & Scarsini, Marco, 2005. "A folk theorem for minority games," Games and Economic Behavior, Elsevier, vol. 53(2), pages 208-230, November.
    30. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
    31. Claudio Mattalia, 2003. "Existence of solutions and asset pricing bubbles in general equilibrium models," ICER Working Papers - Applied Mathematics Series 02-2003, ICER - International Centre for Economic Research.
    32. Salvatore Modica & Marco Scarsini, 2003. "The convexity-cone approach to comparative risk and downside risk," ICER Working Papers - Applied Mathematics Series 01-2003, ICER - International Centre for Economic Research.
    33. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    34. Umberto Cherubini & Elisa Luciano, 2003. "Pricing Vulnerable Options With Copulas," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 5(1), pages 27-39, April.
    35. Guido Cozzi & Fabio Privileggi, 2002. "Wealth Polarization and Pulverization in Fractal Societies," ICER Working Papers - Applied Mathematics Series 39-2002, ICER - International Centre for Economic Research.
    36. Massimo Marinacci & Luigi Montrucchio, 2003. "Ultramodular functions," ICER Working Papers - Applied Mathematics Series 13-2003, ICER - International Centre for Economic Research.
    37. Enrico Diecidue & Fabio Maccheroni, 2002. "Coherence without Additivity," ICER Working Papers - Applied Mathematics Series 10-2002, ICER - International Centre for Economic Research.
    38. Fabio Maccheroni & Fabio Maccheroni & Massimo Marinacci & Massimo Marinacci, 2003. "How to cut a pizza fairly: Fair division with decreasing marginal evaluations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 457-465, June.
    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. Gajdos, Thibault & Maurin, Eric, 2004. "Unequal uncertainties and uncertain inequalities: an axiomatic approach," Journal of Economic Theory, Elsevier, vol. 116(1), pages 93-118, May.
    2. Müller, Alfred & Scarsini, Marco, 2005. "Archimedean copulæ and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 434-445, April.
    3. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "Contributions to the understanding of Bayesian consistency," ICER Working Papers - Applied Mathematics Series 13-2004, ICER - International Centre for Economic Research.
    4. Taizhong Hu & Alfred Müller & Marco Scarsini, 2002. "Some Counterexamples in Positive Dependence," ICER Working Papers - Applied Mathematics Series 28-2003, ICER - International Centre for Economic Research, revised Jul 2003.
    5. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On consistency of nonparametric normal mixtures for Bayesian density estimation," ICER Working Papers - Applied Mathematics Series 23-2004, ICER - International Centre for Economic Research.
    6. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On rates of convergence for posterior distributions in infinite–dimensional models," ICER Working Papers - Applied Mathematics Series 24-2004, ICER - International Centre for Economic Research.
    7. Renault, Jerome & Scarlatti, Sergio & Scarsini, Marco, 2005. "A folk theorem for minority games," Games and Economic Behavior, Elsevier, vol. 53(2), pages 208-230, November.
    8. Salvatore Modica & Marco Scarsini, 2003. "The convexity-cone approach to comparative risk and downside risk," ICER Working Papers - Applied Mathematics Series 01-2003, ICER - International Centre for Economic Research.
    9. Castagnoli, Erio & Maccheroni, Fabio & Marinacci, Massimo, 2002. "Insurance premia consistent with the market," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 267-284, October.
    10. Enrico Diecidue & Fabio Maccheroni, 2002. "Coherence without Additivity," ICER Working Papers - Applied Mathematics Series 10-2002, ICER - International Centre for Economic Research.
    11. Gajdos, T. & Hayashi, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Attitude toward imprecise information," Journal of Economic Theory, Elsevier, vol. 140(1), pages 27-65, May.
    12. Izhakian, Yehuda, 2017. "Expected utility with uncertain probabilities theory," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 91-103.
    13. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications,, Elsevier.
    14. Thibault Gajdos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2002. "Coping with imprecise information: a decision theoretic approach," Cahiers de la Maison des Sciences Economiques v04056, Université Panthéon-Sorbonne (Paris 1), revised May 2004.
    15. Klaus Nehring, 2006. "Decision-Making in the Context of Imprecise Probabilistic Beliefs," Economics Working Papers 0034, Institute for Advanced Study, School of Social Science.
    16. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    17. 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.
    18. Chateauneuf, Alain & Faro, José Heleno, 2009. "Ambiguity through confidence functions," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 535-558, September.
    19. Peter Klibanoff & Sujoy Mukerji & Kyoungwon Seo, 2014. "Perceived Ambiguity and Relevant Measures," Econometrica, Econometric Society, vol. 82(5), pages 1945-1978, September.
    20. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2011. "Rational preferences under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 341-375, October.

    More about this item

    Keywords

    Uncertainty; Decision; Multiple Priors;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:icr:wpmath:18-2003. 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: Daniele Pennesi (email available below). General contact details of provider: https://edirc.repec.org/data/icerrit.html .

    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.