Convex integral functionals of regular processes

This article gives dual representations for convex integral functionals on the linear space of regular processes. This space turns out to be a Banach space containing many more familiar classes of stochastic processes and its dual is identified with the space of optional Radon measures with essentially bounded variation. Combined with classical Banach space techniques, our results allow for systematic treatment of a large class of optimization problems from optimal stopping to singular stochastic control and financial mathematics.