Expected Utility Optimization with Stochastically Ordered Returns

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 optimizes 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 optimization 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 an economic application by considering the optimal production problem of competitive firms