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Multi stage stochastic programs arise in many applications from engineeringwhenever a set of inventories or stocks has to be valued. Such is the case inseasonal storage valuation of a set of cascaded reservoir chains in hydromanagement. A popular method is Stochastic Dual Dynamic Programming (SDDP),especially when the dimensionality of the problem is large and Dynamicprogramming no longer an option. The usual assumption of SDDP is thatuncertainty is stage-wise independent, which is highly restrictive from apractical viewpoint. When possible, the usual remedy is to increase thestate-space to account for some degree of dependency. In applications this maynot be possible or it may increase the state space by too much. In this paperwe present an alternative based on keeping a functional dependency in the SDDP- cuts related to the conditional expectations in the dynamic programmingequations. Our method is based on popular methodology in mathematical finance,where it has progressively replaced scenario trees due to superior numericalperformance. On a set of numerical examples, we too show the interest of thisway of handling dependency in uncertainty, when combined with SDDP. Our methodis readily available in the open source software package StOpt.

On conditional cuts for Stochastic Dual Dynamic Programming