IDEAS home Printed from https://ideas.repec.org/a/nea/journl/y2024i65p12-29.html
   My bibliography  Save this article

On decision making in probability models with uncertainty

Author

Listed:
  • Shiryaev, A.

    (Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
    Lomonosov Moscow State University, Moscow, Russia)

Abstract

In the modern theory of probability the basic notion is "probabilistic space" on which the notions of random variables and their expectations are defi ned. These elements give, in particular, a possibility to determine the quality of decisions, to defi ne decision functions and their quality. At the same time in probability models with uncertainty we need to consider instead of one probability space a family of such spaces. For this case of uncertainty we have notions of sublinear and nonlinear expectations, g-expectations, backward stochastic differential equations, notions of Choquet capacity and integrals. The classical law of large number has a new form under assumption of uncertainty. The present paper has an overview character and is aimed to attract the readers' attention to new probabilistic aspects of modeling under uncertainty and to corresponding tools of investigation. The paper is an extended version of the author's report at the seminar on mathematical economics of V. I. Danilov and V. M. Polterovich at Moscow School of Economics, MSU, given on 30 January 2024.

Suggested Citation

  • Shiryaev, A., 2024. "On decision making in probability models with uncertainty," Journal of the New Economic Association, New Economic Association, vol. 65(4), pages 12-29.
    • Handle: RePEc:nea:journl:y:2024:i:65:p:12-29
    DOI: 10.31737/22212264_2024_4_12-29
    as

    Download full text from publisher

    File URL: http://www.econorus.org/repec/journl/2024-65-12-29r.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.31737/22212264_2024_4_12-29?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. 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.
    2. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, 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. Kiyohiko G. Nishimura & Hiroyuki Ozaki, 2001. "Search under the Knightian Uncertainty," CIRJE F-Series CIRJE-F-112, CIRJE, Faculty of Economics, University of Tokyo.
    2. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
    3. André Lapied & Thomas Rongiconi, 2013. "Ambiguity as a Source of Temptation: Modeling Unstable Beliefs," Working Papers halshs-00797631, HAL.
    4. Attanasi, Giuseppe Marco & Montesano, Aldo, 2010. "The Price for Information about Probabilities and its Relation with Capacities," TSE Working Papers 10-193, Toulouse School of Economics (TSE).
    5. Vassili Vergopoulos, 2014. "A Behavioral Definition of States of the World," Documents de travail du Centre d'Economie de la Sorbonne 14047, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    6. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    7. Jewitt, Ian & Mukerji, Sujoy, 2017. "Ordering ambiguous acts," Journal of Economic Theory, Elsevier, vol. 171(C), pages 213-267.
    8. Florian Mudekereza, 2025. "Robust Social Planning," Papers 2504.07401, arXiv.org.
    9. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2016. "A life-cycle model with ambiguous survival beliefs," Journal of Economic Theory, Elsevier, vol. 162(C), pages 137-180.
    10. Claudio A. Bonilla & Pablo A. Gutiérrez Cubillos, 2021. "The effects of ambiguity on entrepreneurship," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 30(1), pages 63-80, February.
    11. Zimper, Alexander, 2012. "Asset pricing in a Lucas fruit-tree economy with the best and worst in mind," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 610-628.
    12. Crès, Hervé & Tvede, Mich, 2022. "Aggregation of opinions in networks of individuals and collectives," Journal of Economic Theory, Elsevier, vol. 199(C).
    13. Gérard Mondello, 2020. "Building Belief Systems and Medical Ethics: The Covid-19 Controversies," GREDEG Working Papers 2020-35, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    14. Yoram Halevy & Vincent Feltkamp, 2005. "A Bayesian Approach to Uncertainty Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(2), pages 449-466.
    15. Alexander Zimper, 2011. "Re-examining the law of iterated expectations for Choquet decision makers," Theory and Decision, Springer, vol. 71(4), pages 669-677, October.
    16. Basieva, Irina & Khrennikova, Polina & Pothos, Emmanuel M. & Asano, Masanari & Khrennikov, Andrei, 2018. "Quantum-like model of subjective expected utility," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 150-162.
    17. Jürgen Eichberger & David Kelsey, 2014. "Optimism And Pessimism In Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(2), pages 483-505, May.
    18. Faro, José Heleno & Lefort, Jean-Philippe, 2019. "Dynamic objective and subjective rationality," Theoretical Economics, Econometric Society, vol. 14(1), January.
    19. Javier D. Donna, 2024. "Redistributive politics under ambiguity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 62(3), pages 583-607, May.
    20. 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.

    More about this item

    Keywords

    probabilistic-uncertain models; utility functions; Allais and Ellsberg paradoxes; capacity and Choquet integral; inverse stochastic differential equations; upper and lower prices;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

    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:nea:journl:y:2024:i:65:p:12-29. 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: Alexey Tcharykov (email available below). General contact details of provider: https://edirc.repec.org/data/nearuea.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.