Convex Stochastic Optimization

This chapter gives a general formulation of convex stochastic optimization problems in finite discrete time. The objective of the minimization problem is an integral functional given in terms of a convex normal integrand. The bulk of the chapter consists a review of the theory of normal integrands, random sets and integral functionals that will be used throughout the book. The last section illustrates the generality of the framework by expressing classical problem formats from mathematical programming, optimal stopping, optimal control and financial mathematics as problems of convex stochastic optimization. The general format of convex stochastic optimization allows also for various extensions to the classical formulations.