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...

We consider stochastic optimization problems involving stochastic dominance constraints of first order, also called stochastic ordering constraints. They are equivalent to a continuum of probabilistic constraints or chance constraints. We develop first order necessary and sufficient conditions...

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...