Expected utility maximization with stochastically ordered returns

Romain Gauchon (1) , Karim Barigou (1)

1 ISFA - Institut de Science Financière et d'Assurances

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.

Mots clés: Convolution order; Expected utility; Fractional calculus; Prevention

Domaines: Gestion des risques [q-fin.RM]; Probabilités [math.PR]

Romain Gauchon, Karim Barigou. Expected utility maximization with stochastically ordered returns. 2021. ⟨hal-03295594⟩