SDDP for multistage stochastic linear programs based on spectral risk measures

We consider risk-averse formulations of multistage stochastic linear programs. For these formulations, based on convex combinations of spectral risk measures, risk-averse dynamic programming 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 recourse functions. This allows us to define a risk-averse nonanticipative feasible policy for the stochastic linear program. Formulas for the cuts that approximate the recourse functions are given. In particular, we show that some of the cut coefficients have analytic formulas. AMS subject classifications: 90C15, 91B30.