  This article presents a new method for computing guaranteed convex and
concave relaxations of nonlinear stochastic optimal control problems with
final-time expected-value cost functions. This method is motivated by similar
methods for deterministic optimal control problems, which have been
successfully applied within spatial branch-and-bound (B&B) techniques to obtain
guaranteed global optima. Relative to those methods, a key challenge here is
that the expected-value cost function cannot be expressed analytically in
closed form. Nonetheless, the presented relaxations provide rigorous lower and
upper bounds on the optimal objective value with no sample-based approximation
error. In principle, this enables the use of spatial B&B global optimization
techniques, but we leave the details of such an algorithm for future work.
