Expected Utility Optimization with Convolutional Stochastically Ordered Returns

Romain Gauchon and Karim Barigou ()
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Romain Gauchon: ISFA, Université Lyon 1, UCBL, LSAF EA2429, F-69007 Lyon, France
Karim Barigou: École d’actuariat, Université Laval, 2425, Rue de l’Agriculture, Québec, QC G1V 0A6, Canada

Risks, 2024, vol. 12, issue 6, 1-19

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.

Keywords: stochastic orders; expected utility; optimization (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2024
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