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Information relaxation and duality in Markov decision processes have beenstudied recently by several researchers with the goal to derive dual bounds onthe value function. In this paper we extend this dual formulation to controlledMarkov diffusions: in a similar way we relax the constraint that the decisionshould be made based on the current information and impose penalty to punishthe access to the information in advance. We establish the weak duality, strongduality and complementary slackness results in a parallel way as those inMarkov decision processes. We explore the structure of the optimal penaltiesand expose the connection between Markov decision processes and controlledMarkov diffusions. We demonstrate the use of the dual representation forcontrolled Markov diffusions in a classic dynamic portfolio choice problem. Weevaluate the lower bounds on the expected utility by Monte Carlo simulationunder a sub-optimal policy, and we propose a new class of penalties to deriveupper bounds with little extra computation. The small gaps between the lowerbounds and upper bounds indicate that the available policy is near optimal aswell as the effectiveness of our proposed penalty in the dual method.

Information Relaxation and Dual Formulation of Controlled Markov Diffusions