Generalized Bounds for Convex Multistage Stochastic Programs

This book investigates convex multistage stochastic programs whose objective and constraint functions exhibit a generalized nonconvex dependence on the random parameters. Although the classical Jensen and Edmundson-Madansky type bounds or its extensions are generally not available for such problems, tight bounds can systematically be constructed under mild regularity conditions. A nice primal-dual symmetry property is revealed when the proposed bounding method is applied to linear stochastic programs. After having developed the theoretical concepts, exemplary real-life applications are studied. It is shown how market power, lognormal stochastic processes, and risk-aversion can be properly handled in a stochastic programming framework. Numerical experiments show that the relative gap between the bounds can be reduced to a few percent without exploding the problem size.