Solvability of Forward-Backward SDEs and the Nodal Set of Hamilton-Jacobi-Bellman Equations
نویسنده
چکیده
Abstract. In this paper, the solvability of a class of forward-backward stochastic di erential equations (SDEs for short) over an arbitrarily prescribed time duration is studied. We design a stochastic relaxed control problem, with both drift and di usion all being controlled, so that the solvability problem is converted to a problem of nding the nodal set of the viscosity solution to a certain Hamilton-Jacobi-Bellman equation. Our method overcomes the fatal di culty encountered in the traditional contraction mapping theorem approach to the existence theorem of such SDEs.
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