We show that the main results of the expected utility and dual utility theories can be derived in a unified way from two fundamental mathematical ideas: the separation principle of convex analysis, and integral representations of continuous linear functionals from functional analysis. Our analysis reveals the dual character of utility functions. We also derive new … Read more
In this paper we study linear optimization problems with multi-dimensional linear positive second-order stochastic dominance constraints. By using the polyhedral properties of the second- order linear dominance condition we present a cutting-surface algorithm, and show its finite convergence. The cut generation problem is a difference of convex functions (DC) optimization problem. We exploit the polyhedral … Read more
We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution. We propose a new portfolio optimization model involving stochastic dominance constraints on the portfolio return. We develop optimality and duality theory for these models. We construct equivalent optimization models with utility functions. Numerical illustration … Read more