  This article studies optional and predictable projections of integrands and
convex-valued stochastic processes. The existence and uniqueness are shown
under general conditions that are analogous to those for conditional
expectations of integrands and random sets. In the convex case, duality
correspondences between the projections and projections of epigraphs are given.
These results are used to study projections of set-valued integrands.
Consistently with the general theory of stochastic processes, projections are
not constructed using reference measures on the optional and predictable
sigma-algebras.

Probability;Optimization and Control