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 sets defined by the usual stochastic ordering relation and by the second order stochastic dominance relation. Under fairy general assumptions we prove that in the space of integrable random variables the closed convex hull of the first set is equal to the second set.

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...