Statistical approximations for recourse constrained stochastic programs

The two stage stochastic program with recourse is known to have numerous applications in financial planning, energy modeling, telecommunications systems etc. Notwithstanding its applicability, the two stage stochastic program is limited in its ability to incorporate a decision maker’s attitudes towards risk. In this paper the authors present an extension via the inclusion of a recourse constraint. This results in a convex integrated chance constraint (ICC), which inherits the convexity properties of two stage programs. However, it also inherits some of the difficulties associated with the evaluation of recourse functions. This motivates the present study of conditions that may be applicable to algorithms using statistical approximations of such ICC. The authors present a set of sufficient conditions that these approximations may satisfy in order to assure convergence. The present conditions are satisfied by a wide range of statistical approximations, and they demonstrate that these approximations can be generated within standard algorithmic procedures.