Dual Formulation of Controlled Markov Diffï¿1⁄2usions and Its Application

Information relaxation and duality in Markov decision processes have been studied recently to derive upper bounds on the maximal expected reward (or lower bounds on the minimal expected cost). The idea is to relax the non-anticipativity constraint on the controls and impose a penalty to punish such a violation. In this paper we generalize this dual approach to controlled Markov diffusions. We develop the weak duality and strong duality results, and explore the structure of the optimal penalty. We demonstrate the use of this dual formulation by computing upper bounds on the optimal expected utility in a dynamic portfolio choice problem.