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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
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    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. 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. 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..
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