SDDP for multistage stochastic linear programs based on spectral risk measures

Abstract

We consider risk-averse formulations of multistage stochastic linear programs. Forthese formulations, based on convex combinations of spectral risk measures, risk-averse dynamicprogramming equations can be written. As a result, the Stochastic Dual Dynamic Programming(SDDP) algorithm can be used to obtain approximations of the corresponding risk-averse recoursefunctions. This allows us to define a risk-averse nonanticipative feasible policy for the stochasticlinear program. Formulas for the cuts that approximate the recourse functions are given.