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Stochastic Target Problems, Dynamic Programming, and Viscosity Solutions

In this paper, we define and study a new class of optimal stochastic control problems which is closely related to the theory of Backward SDE's and forward-backward SDE's. The controlled process takes values in RXR and a given initial data for X(O). Then, the control problem is to find the minimal initial data for Y so that it reaches a stochastic target at a specified terminal time T.