  This article studies convex duality in stochastic optimization over finite
discrete-time. The first part of the paper gives general conditions that yield
explicit expressions for the dual objective in many applications in operations
research and mathematical finance. The second part derives optimality
conditions by combining general saddle-point conditions from convex duality
with the dual representations obtained in the first part of the paper. Several
applications to stochastic optimization and mathematical finance are given.
