  This paper studies duality and optimality conditions in general convex
stochastic optimization problems introduced by Rockafellar and Wets in 1976. We
derive an explicit dual problem in terms of two dual variables, one of which is
the shadow price of information while the other one gives the marginal cost of
a perturbation much like in classical Lagrangian duality. Existence of primal
solutions and the absence of duality gap are obtained without compactness or
boundedness assumptions. In the context of financial mathematics, the relaxed
assumptions are satisfied under the well-known no-arbitrage condition and the
reasonable asymptotic elasticity condition of the utility function. We extend
classical portfolio optimization duality theory to problems of optimal
semi-static hedging. Besides financial mathematics, we obtain several new
frameworks in stochastic programming and stochastic optimal control.
