IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v12y2024i6p95-d1414649.html
   My bibliography  Save this article

Expected Utility Optimization with Convolutional Stochastically Ordered Returns

Author

Listed:
  • Romain Gauchon

    (ISFA, Université Lyon 1, UCBL, LSAF EA2429, F-69007 Lyon, France
    These authors contributed equally to this work.)

  • Karim Barigou

    (École d’actuariat, Université Laval, 2425, Rue de l’Agriculture, Québec, QC G1V 0A6, Canada
    These authors contributed equally to this work.)

Abstract

Expected utility theory is critical for modeling rational decision making under uncertainty, guiding economic agents as they seek to optimize outcomes. Traditional methods often require restrictive assumptions about underlying stochastic processes, limiting their applicability. This paper expands the theoretical framework by considering investment returns modeled by a stochastically ordered family of random variables under the convolution order, including Poisson, Gamma, and exponential distributions. Utilizing fractional calculus, we derive explicit, closed-form expressions for the derivatives of expected utility for various utility functions, significantly broadening the potential for analytical and computational applications. We apply these theoretical advancements to a case study involving the optimal production strategies of competitive firms, demonstrating the practical implications of our findings in economic decision making.

Suggested Citation

  • Romain Gauchon & Karim Barigou, 2024. "Expected Utility Optimization with Convolutional Stochastically Ordered Returns," Risks, MDPI, vol. 12(6), pages 1-19, June.
    • Handle: RePEc:gam:jrisks:v:12:y:2024:i:6:p:95-:d:1414649
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/12/6/95/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/12/6/95/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Shaked, Moshe & Suarez-Llorens, Alfonso, 2003. "On the Comparison of Reliability Experiments Based on the Convolution Order," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 693-702, January.
    2. Sandmo, Agnar, 1971. "On the Theory of the Competitive Firm under Price Uncertainty," American Economic Review, American Economic Association, vol. 61(1), pages 65-73, March.
    3. Ehrlich, Isaac & Becker, Gary S, 1972. "Market Insurance, Self-Insurance, and Self-Protection," Journal of Political Economy, University of Chicago Press, vol. 80(4), pages 623-648, July-Aug..
    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. Fatma Lajeri-Chaherli, 2016. "On The Concavity And Quasiconcavity Properties Of ( Σ , Μ ) Utility Functions," Bulletin of Economic Research, Wiley Blackwell, vol. 68(3), pages 287-296, April.
    2. 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.
    3. Eichner, Thomas & Wagener, Andreas, 2011. "Increases in skewness and three-moment preferences," Mathematical Social Sciences, Elsevier, vol. 61(2), pages 109-113, March.
    4. Quiggin, John C. & Chambers, Robert G., 2004. "Drought policy: a graphical analysis," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 48(2), pages 1-27.
    5. Thomas Eichner & Andreas Wagener, 2002. "Increases in Risk and the Welfare State," CESifo Working Paper Series 685, CESifo.
    6. Raushan Bokusheva & Lukáš Čechura & Subal C. Kumbhakar, 2023. "Estimating persistent and transient technical efficiency and their determinants in the presence of heterogeneity and endogeneity," Journal of Agricultural Economics, Wiley Blackwell, vol. 74(2), pages 450-472, June.
    7. Huang-Meier, Winifred & Freeman, Mark C., 2015. "Aggregate dividends and consumption smoothing," International Review of Financial Analysis, Elsevier, vol. 42(C), pages 324-335.
    8. Park, Timothy A. & Antonovitz, Frances, 1991. "Econometric Tests Of Firm Decision Making Under Uncertainty: Optimal Output And Hedging Decisions," 1991 Annual Meeting, August 4-7, Manhattan, Kansas 271264, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    9. Barrett, Christopher B., 1999. "The effects of real exchange rate depreciation on stochastic producer prices in low-income agriculture," Agricultural Economics, Blackwell, vol. 20(3), pages 215-230, May.
    10. Martín Egozcue & Xu Guo & Wing-Keung Wong, 2015. "Optimal output for the regret-averse competitive firm under price uncertainty," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 5(2), pages 279-295, December.
    11. Burton, Diana M. & Love, H. Alan, 1996. "A Review of Alternative Expectations Regimes in Commodity Markets: Specification, Estimation, and Hypothesis Testing Using Structural Models," Agricultural and Resource Economics Review, Cambridge University Press, vol. 25(2), pages 213-231, October.
    12. Romain Gauchon & Karim Barigou, 2024. "Expected utility maximization with stochastically ordered returns," Post-Print hal-03295594, HAL.
    13. Allen, W. David, 2013. "Self-protection against crime victimization: Theory and evidence from university campuses," International Review of Law and Economics, Elsevier, vol. 34(C), pages 21-33.
    14. Heyes, Anthony & Rickman, Neil & Tzavara, Dionisia, 2004. "Legal expenses insurance, risk aversion and litigation," International Review of Law and Economics, Elsevier, vol. 24(1), pages 107-119, March.
    15. Thomas Eichner & Rüdiger Pethig, 2015. "Efficient Management of Insecure Fossil Fuel Imports through Taxing Domestic Green Energy?," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 17(5), pages 724-751, October.
    16. Agarwal, Sumit & Satyanarain, Rengarajan & Sing, Tien Foo & Vollmer, Derek, 2016. "Effects of construction activities on residential electricity consumption: Evidence from Singapore's public housing estates," Energy Economics, Elsevier, vol. 55(C), pages 101-111.
    17. Ehrlich, Isaac & Yin, Yong, 2018. "The problem of the uninsured," Research in Economics, Elsevier, vol. 72(1), pages 147-168.
    18. Haile, M.G. & Kalkuhl, M., 2014. "Volatility in the international food markets: implications for global agricultural supply and for market and price policy," Proceedings “Schriften der Gesellschaft für Wirtschafts- und Sozialwissenschaften des Landbaues e.V.”, German Association of Agricultural Economists (GEWISOLA), vol. 49, March.
    19. Z. Bar‐Shira & R.E. Just & D. Zilberman, 1997. "Estimation of farmers' risk attitude: an econometric approach," Agricultural Economics, International Association of Agricultural Economists, vol. 17(2-3), pages 211-222, December.
    20. Eeckhoudt, Louis & Gollier, Christian & Schlesinger, Harris, 1997. "The no-loss offset provision and the attitude towards risk of a risk-neutral firm," Journal of Public Economics, Elsevier, vol. 65(2), pages 207-217, August.

    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:gam:jrisks:v:12:y:2024:i:6:p:95-:d:1414649. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.