Abstract
This paper is devoted to the investigation of the second-order necessary conditions of singular control problems for controlled forward-backward delay systems in the case where the control domain is non-convex and the diffusion coefficients are independent of control. A second-order matrix-valued adjoint system is constructed to solve the obstacle caused by the product of the solution and its delay counterpart of the first-order variational equations. With the help of this observation, the second-order expansion of cost functional Yε and the stochastic maximum principle are proved. Our work generalizes the classical case to the delay case
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