  Multi stage stochastic programs arise in many applications from engineering
whenever a set of inventories or stocks has to be valued. Such is the case in
seasonal storage valuation of a set of cascaded reservoir chains in hydro
management. A popular method is Stochastic Dual Dynamic Programming (SDDP),
especially when the dimensionality of the problem is large and Dynamic
programming no longer an option. The usual assumption of SDDP is that
uncertainty is stage-wise independent, which is highly restrictive from a
practical viewpoint. When possible, the usual remedy is to increase the
state-space to account for some degree of dependency. In applications this may
not be possible or it may increase the state space by too much. In this paper
we present an alternative based on keeping a functional dependency in the SDDP
- cuts related to the conditional expectations in the dynamic programming
equations. Our method is based on popular methodology in mathematical finance,
where it has progressively replaced scenario trees due to superior numerical
performance. On a set of numerical examples, we too show the interest of this
way of handling dependency in uncertainty, when combined with SDDP. Our method
is readily available in the open source software package StOpt.
