Abstract
Optimization problems over processes of bounded variation arise naturally in many applications from optimal stopping to optimal investment under transaction costs. This paper gives dual representations for convex functionals over the linear space of BV processes with essentially bounded variation. This space is identified as the Banach dual of the space of Regular processes. Combined with well-known 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. This is joint work with Ari-Pekka Perkkiö.