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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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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.
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    Cited by:

    1. Naudé, Wim, 2023. "Artificial Intelligence and the Economics of Decision-Making," IZA Discussion Papers 16000, Institute of Labor Economics (IZA).

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    More about this item

    Keywords

    Convolution order; Expected utility; Fractional calculus; Prevention;
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