IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/69363.html

Measuring utility without mixing apples and oranges and eliciting beliefs about stock prices

Author

Listed:
  • O'Callaghan, Patrick

Abstract

In day-to-day life we encounter decisions amongst prospects that do not have a convex structure. To address this concern, Herstein and Milnor introduce mixture sets and provide necessary and sufficient conditions for a cardinal and linear utility representation. We derive the same utility representation for partial mixture sets: where the mixture operation is only partially defined. The resulting model has an interesting application to finance. In particular, we use paths instead of events to elicit utility and beliefs about stock prices. This feature is promising for settings where the dimension of the state space is large.

Suggested Citation

  • O'Callaghan, Patrick, 2016. "Measuring utility without mixing apples and oranges and eliciting beliefs about stock prices," MPRA Paper 69363, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:69363
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/69363/1/MPRA_paper_69363.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Karni, Edi & Safra, Zvi, 2000. "An extension of a theorem of von Neumann and Morgenstern with an application to social choice theory," Journal of Mathematical Economics, Elsevier, vol. 34(3), pages 315-327, November.
    2. Simon Grant & Atsushi Kajii & Ben Polak & Zvi Safra, 2010. "Generalized Utilitarianism and Harsanyi's Impartial Observer Theorem," Econometrica, Econometric Society, vol. 78(6), pages 1939-1971, November.
    3. Michael Richter & Ariel Rubinstein, 2015. "Back to Fundamentals: Equilibrium in Abstract Economies," American Economic Review, American Economic Association, vol. 105(8), pages 2570-2594, August.
    4. Rockinger, Michael & Jondeau, Eric, 2002. "Entropy densities with an application to autoregressive conditional skewness and kurtosis," Journal of Econometrics, Elsevier, vol. 106(1), pages 119-142, January.
    5. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345, January.
    6. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    7. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
    8. Seok Young Hong & Oliver Linton & Hui Jun Zhang, 2015. "An investigation into multivariate variance ratio statistics and their application to stock market predictability," CeMMAP working papers 13/15, Institute for Fiscal Studies.
    9. Inoue, Tomoki, 2010. "A utility representation theorem with weaker continuity condition," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 122-127, January.
    10. 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..
    11. Monteiro, Paulo Klinger, 1987. "Some results on the existence of utility functions on path connected spaces," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 147-156, April.
    12. Fishburn, P. C., 1983. "Utility functions on ordered convex sets," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 221-232, December.
    13. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
    14. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    15. Jack Stecher & Timothy Shields & John Dickhaut (deceased), 2011. "Generating Ambiguity in the Laboratory," Management Science, INFORMS, vol. 57(4), pages 705-712, April.
    16. Edi Karni, 2009. "A theory of medical decision making under uncertainty," Journal of Risk and Uncertainty, Springer, vol. 39(1), pages 1-16, August.
    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. O’Callaghan, Patrick H., 2018. "Axioms for measuring utility on partial mixture sets," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 76-86.
    2. O'Callaghan, Patrick, 2017. "Axioms for Measuring without mixing apples and Oranges," MPRA Paper 81196, University Library of Munich, Germany.
    3. Gayer, Gabrielle, 2010. "Perception of probabilities in situations of risk: A case based approach," Games and Economic Behavior, Elsevier, vol. 68(1), pages 130-143, January.
    4. Grant Simon & Guerdjikova Ani & Quiggin John, 2021. "Ambiguity and Awareness: A Coherent Multiple Priors Model," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 21(2), pages 571-612, June.
    5. Beissner, Patrick & Werner, Jan, 2023. "Optimal allocations with α-MaxMin utilities, Choquet expected utilities, and Prospect Theory," Theoretical Economics, Econometric Society, vol. 18(3), July.
    6. Itzhak Gilboa & Andrew Postlewaite & Larry Samuelson & David Schmeidler, 2019. "What are axiomatizations good for?," Theory and Decision, Springer, vol. 86(3), pages 339-359, May.
    7. O’Callaghan, Patrick, 2011. "Context and Decision: Utility on a Union of Mixture Spaces," The Warwick Economics Research Paper Series (TWERPS) 973, University of Warwick, Department of Economics.
    8. O'Callaghan, Patrick, 2011. "Context and Decision: Utility on a Union of Mixture Spaces," Economic Research Papers 270751, University of Warwick - Department of Economics.
    9. Lovric, M. & Kaymak, U. & Spronk, J., 2008. "A Conceptual Model of Investor Behavior," ERIM Report Series Research in Management ERS-2008-030-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    10. Gilboa, Itzhak & Samuelson, Larry & Schmeidler, David, 2013. "Dynamics of inductive inference in a unified framework," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1399-1432.
    11. Massimiliano Amarante & Mario Ghossoub & Edmund Phelps, 2012. "Contracting for Innovation under Knightian Uncertainty," Cahiers de recherche 18-2012, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    12. Thierry Chauveau & Nicolas Nalpas, 1999. "Risk Weighted Utility Theory as a Solution to the Equity Premium Puzzle," Cahiers de la Maison des Sciences Economiques bla99020, Université Panthéon-Sorbonne (Paris 1).
    13. 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.
    14. 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.
    15. 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.
    16. Riddel, Mary C. & Shaw, W. Douglass, 2006. "A Theoretically-Consistent Empirical Non-Expected Utility Model of Ambiguity: Nuclear Waste Mortality Risk and Yucca Mountain," Pre-Prints 23964, Texas A&M University, Department of Agricultural Economics.
    17. Yehuda Izhakian, 2012. "Ambiguity Measurement," Working Papers 12-01, New York University, Leonard N. Stern School of Business, Department of Economics.
    18. 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.
    19. Ivan Moscati, 2022. "Behavioral and heuristic models are as-if models too — and that’s ok," BAFFI CAREFIN Working Papers 22177, BAFFI CAREFIN, Centre for Applied Research on International Markets Banking Finance and Regulation, Universita' Bocconi, Milano, Italy.
    20. repec:rza:wpaper:296 is not listed on IDEAS
    21. Epper, Thomas & Fehr-Duda, Helga, 2017. "A Tale of Two Tails: On the Coexistence of Overweighting and Underweighting of Rare Extreme Events," Economics Working Paper Series 1705, University of St. Gallen, School of Economics and Political Science.

    More about this item

    Keywords

    ;
    ;
    ;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C9 - Mathematical and Quantitative Methods - - Design of Experiments
    • D8 - Microeconomics - - Information, Knowledge, 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:pra:mprapa:69363. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.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.