Stochastic Verification Theorem of Forward-Backward Controlled Systems for Viscosity Solutions

In this paper, we investigate the controlled system described by forward-backward stochastic differential equations with the control contained in drift, diffusion and generator of BSDE. A new verification theorem is derived within the framework of viscosity solutions without involving any derivatives of the value functions. It is worth to pointing out that this theorem has wider applicability than the restrictive classical verification theorems. As a relevant problem, the optimal stochastic feedback controls for forward-backward system are discussed as well.

💡 Research Summary

In this paper the authors consider a very general stochastic optimal control problem in which the control enters not only the drift and diffusion coefficients of a forward stochastic differential equation (SDE) but also the generator of a backward stochastic differential equation (BSDE). The state dynamics are described by
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