IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-03295594.html
   My bibliography  Save this paper

Expected utility maximization with stochastically ordered returns

Author

Listed:
  • Romain Gauchon

    (ISFA - Institut de Science Financière et d'Assurances)

  • Karim Barigou

    (ISFA - Institut de Science Financière et d'Assurances)

Abstract

Expected utility is an influential theory to study rational choice among risky assets. For each investment, an economic agent expects to receive a random payoff and therefore maximizes its expected utility. To the best of our knowledge, there exists no general procedure to take the derivative of the expected utility as a function of the investment without heavy assumptions on the underlying processes. This article considers expected utility maximization when payoffs are modeled by a family of random variables increasing with investment for the convolution order such as Poisson, Gamma or Exponential distributions. For several common utility functions, with the help of fractional calculus, we manage to obtain closed-form formulas for the expected utility derivative. The paper also provides two economic applications: production of competitive firms and investment in prevention.

Suggested Citation

  • Romain Gauchon & Karim Barigou, 2021. "Expected utility maximization with stochastically ordered returns," Working Papers hal-03295594, HAL.
    • Handle: RePEc:hal:wpaper:hal-03295594
    Note: View the original document on HAL open archive server: https://hal.science/hal-03295594
    as

    Download full text from publisher

    File URL: https://hal.science/hal-03295594/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Altonji, Joseph G, 1993. "The Demand for and Return to Education When Education Outcomes Are Uncertain," Journal of Labor Economics, University of Chicago Press, vol. 11(1), pages 48-83, January.
    2. Christophe Courbage, 2001. "Self-Insurance, Self-Protection and Market Insurance within the Dual Theory of Choice," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 26(1), pages 43-56, June.
    3. Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-1277, November.
    4. Eric Briys & Harris Schlesinger & J.-Matthias Graf v. d. Schulenburg, 1991. "Reliability of Risk Management: Market Insurance, Self-Insurance and Self-Protection Reconsidered," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 16(1), pages 45-58, June.
    5. Bensalem, Sarah & Santibáñez, Nicolás Hernández & Kazi-Tani, Nabil, 2020. "Prevention efforts, insurance demand and price incentives under coherent risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 369-386.
    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. Naudé, Wim, 2023. "Artificial Intelligence and the Economics of Decision-Making," IZA Discussion Papers 16000, Institute of Labor Economics (IZA).

    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. Courbage, Christophe & Rey, Béatrice & Treich, Nicolas, 2013. "Prevention and precaution," TSE Working Papers 13-445, Toulouse School of Economics (TSE).
    2. Bensalem, Sarah & Santibáñez, Nicolás Hernández & Kazi-Tani, Nabil, 2020. "Prevention efforts, insurance demand and price incentives under coherent risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 369-386.
    3. François Pannequin & Anne Corcos & Claude Montmarquette, 2016. "Behavioral foundations of the substitutability between insurance and self-insurance: An experimental study," CIRANO Working Papers 2016s-12, CIRANO.
    4. Biener, Christian & Eling, Martin & Landmann, Andreas & Pradhan, Shailee, 2018. "Can group incentives alleviate moral hazard? The role of pro-social preferences," European Economic Review, Elsevier, vol. 101(C), pages 230-249.
    5. Sarah Bensalem, 2020. "Self-insurance and Non-concave Distortion Risk Measures," Working Papers hal-02936349, HAL.
    6. Ozlem Ozdemir, 2007. "Valuation of Self-Insurance and Self-Protection under Ambiguity: Experimental Evidence," Jena Economics Research Papers 2007-034, Friedrich-Schiller-University Jena.
    7. Goldzahl, Léontine, 2017. "Contributions of risk preference, time orientation and perceptions to breast cancer screening regularity," Social Science & Medicine, Elsevier, vol. 185(C), pages 147-157.
    8. Jason M. Lindo & Nicholas J. Sanders & Philip Oreopoulos, 2010. "Ability, Gender, and Performance Standards: Evidence from Academic Probation," American Economic Journal: Applied Economics, American Economic Association, vol. 2(2), pages 95-117, April.
    9. Fossen, Frank M. & Glocker, Daniela, 2017. "Stated and revealed heterogeneous risk preferences in educational choice," European Economic Review, Elsevier, vol. 97(C), pages 1-25.
    10. Hugo Pedro Boff, 2004. "The Supply Of Perishable Goods," Econometric Society 2004 Latin American Meetings 306, Econometric Society.
    11. Ralph Stinebrickner & Todd R. Stinebrickner, 2014. "A Major in Science? Initial Beliefs and Final Outcomes for College Major and Dropout," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(1), pages 426-472.
    12. Newbery, David M. & Greve, Thomas, 2017. "The strategic robustness of oligopoly electricity market models," Energy Economics, Elsevier, vol. 68(C), pages 124-132.
    13. Moritz Bohland & Sebastian Schwenen, 2020. "Technology Policy and Market Structure: Evidence from the Power Sector," Discussion Papers of DIW Berlin 1856, DIW Berlin, German Institute for Economic Research.
    14. Bratti, Massimiliano, 2002. "Does the choice of university matter?: a study of the differences across UK universities in life sciences students' degree performance," Economics of Education Review, Elsevier, vol. 21(5), pages 431-443, October.
    15. Christian Gollier & James Hammitt & Nicolas Treich, 2013. "Risk and choice: A research saga," Journal of Risk and Uncertainty, Springer, vol. 47(2), pages 129-145, October.
    16. Romain Gauchon & Karim Barigou, 2024. "Expected utility maximization with stochastically ordered returns," Post-Print hal-03295594, HAL.
    17. John Bound & Michael F. Lovenheim & Sarah Turner, 2010. "Why Have College Completion Rates Declined? An Analysis of Changing Student Preparation and Collegiate Resources," American Economic Journal: Applied Economics, American Economic Association, vol. 2(3), pages 129-157, July.
    18. Committee, Nobel Prize, 2023. "Scientific Background to the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2023," Nobel Prize in Economics documents 2023-2, Nobel Prize Committee.
    19. Fabra, Natalia & Toro, Juan, 2005. "Price wars and collusion in the Spanish electricity market," International Journal of Industrial Organization, Elsevier, vol. 23(3-4), pages 155-181, April.
    20. Fiuza de Bragança, Gabriel Godofredo & Daglish, Toby, 2016. "Can market power in the electricity spot market translate into market power in the hedge market?," Energy Economics, Elsevier, vol. 58(C), pages 11-26.

    More about this item

    Keywords

    Convolution order; Expected utility; Fractional calculus; Prevention;
    All these keywords.

    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:hal:wpaper:hal-03295594. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.