IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2503.13416.html
   My bibliography  Save this paper

Correlation uncertainty: a decision-theoretic approach

Author

Listed:
  • Gerrit Bauch
  • Lorenz Hartmann

Abstract

We provide a decision-theoretic foundation for uncertainty about the correlation structure on a Cartesian product of probability spaces. Our contribution is two-fold: we first provide a full characterization of the set of possible correlations between subspaces as a convex polytope. Its extreme points are identified as the local maxima of mutual information and as maximally zero probability measures. Second, we derive an axiomatic characterization of preferences narrowing down the set of correlations a decision maker considers, making behavior about correlation testable. Thereby, she may regard collections of subspaces as independent from one another. We illustrate our model and results in simple examples on climate change, insurance and portfolio choice.

Suggested Citation

  • Gerrit Bauch & Lorenz Hartmann, 2025. "Correlation uncertainty: a decision-theoretic approach," Papers 2503.13416, arXiv.org.
    • Handle: RePEc:arx:papers:2503.13416
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2503.13416
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Benjamin Enke & Florian Zimmermann, 2019. "Correlation Neglect in Belief Formation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(1), pages 313-332.
    2. Larry G Epstein & Yoram Halevy, 2019. "Ambiguous Correlation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(2), pages 668-693.
    3. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    4. Michel Grabisch & Benjamin Monet & Vassili Vergopoulos, 2023. "Subjective expected utility through stochastic independence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(3), pages 723-757, October.
    5. Monet, Benjamin & Vergopoulos, Vassili, 2022. "Subjective probability and stochastic independence," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    6. Levy, Gilat & Razin, Ronny, 2022. "Combining forecasts in the presence of ambiguity over correlation structures," Journal of Economic Theory, Elsevier, vol. 199(C).
    7. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    8. Ido Kallir & Doron Sonsino, 2009. "The Neglect of Correlation in Allocation Decisions," Southern Economic Journal, John Wiley & Sons, vol. 75(4), pages 1045-1066, April.
    9. Benjamin Monet & Vassili Vergopoulos, 2022. "Subjective probability and stochastic independence," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-04103624, HAL.
    10. Benjamin Monet & Vassili Vergopoulos, 2024. "Ambiguity, randomization and the timing of resolution of uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(4), pages 1021-1045, December.
    11. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    12. Ido Kallir & Doron Sonsino, 2009. "The Neglect of Correlation in Allocation Decisions," Southern Economic Journal, Southern Economic Association, vol. 75(4), pages 1045-1066, April.
    13. Ido Kallir & Doron Sonsino, 2009. "The Neglect of Correlation in Allocation Decisions," Southern Economic Journal, John Wiley & Sons, vol. 75(4), pages 1045-1066, April.
    14. Benjamin Monet & Vassili Vergopoulos, 2022. "Subjective probability and stochastic independence," Post-Print hal-04103624, HAL.
    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. Safra, Zvi & Segal, Uzi, 2022. "A lot of ambiguity," Journal of Economic Theory, Elsevier, vol. 200(C).
    2. Ilke Aydogan & Loïc Berger & Vincent Théroude, 2023. "More Ambiguous or More Complex? An Investigation of Individual Preferences under Uncertainty," Working Papers of BETA 2023-10, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    3. Ilke AYDOGAN & Loïc BERGER & Vincent THEROUDE, 2023. "More Ambiguous or More Complex? An Investigation of Individual Preferences under Model Uncertainty," Working Papers 2023-iRisk-02, IESEG School of Management.
    4. Hossain, Tanjim & Okui, Ryo, 2024. "Belief formation under signal correlation," Games and Economic Behavior, Elsevier, vol. 146(C), pages 160-183.
    5. 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.
    6. ,, 2014. "Second order beliefs models of choice under imprecise risk: non-additive second order beliefs vs. nonlinear second order utility," Theoretical Economics, Econometric Society, vol. 9(3), September.
    7. 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.
    8. Jewitt, Ian & Mukerji, Sujoy, 2017. "Ordering ambiguous acts," Journal of Economic Theory, Elsevier, vol. 171(C), pages 213-267.
    9. Jingyi Xue, 2020. "Preferences with changing ambiguity aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(1), pages 1-60, February.
    10. Marciano Siniscalchi, 2009. "Vector Expected Utility and Attitudes Toward Variation," Econometrica, Econometric Society, vol. 77(3), pages 801-855, May.
    11. Robert Nau, 2001. "De Finetti was Right: Probability Does Not Exist," Theory and Decision, Springer, vol. 51(2), pages 89-124, December.
    12. 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.
    13. 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.
    14. Fabio Maccheroni & Massimo Marinacci & Jingni Yang, 2022. "On the cardinal utility equivalence of biseparable preferences," Theory and Decision, Springer, vol. 92(3), pages 689-701, April.
    15. Calford, Evan M., 2020. "Uncertainty aversion in game theory: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 176(C), pages 720-734.
    16. 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.
    17. R. Luce & A. Marley, 2005. "Ranked Additive Utility Representations of Gambles: Old and New Axiomatizations," Journal of Risk and Uncertainty, Springer, vol. 30(1), pages 21-62, January.
    18. Strzalecki, Tomasz & Werner, Jan, 2011. "Efficient allocations under ambiguity," Journal of Economic Theory, Elsevier, vol. 146(3), pages 1173-1194, May.
    19. Loïc Berger & Louis Eeckhoudt, 2021. "Risk, Ambiguity, and the Value of Diversification," Management Science, INFORMS, vol. 67(3), pages 1639-1647, March.
    20. Song, Yangwei, 2018. "Efficient Implementation with Interdependent Valuations and Maxmin Agents," Rationality and Competition Discussion Paper Series 92, CRC TRR 190 Rationality and Competition.

    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:arx:papers:2503.13416. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.