SOLVABILITY OF FORWARD-BACKWARD SDES AND THE NODAL SET OF HAMILTON-JACOBI-BELLMAN EQUATIONS |
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Authors: | Ma Jin and Yong Jiongmin |
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Institution: | [1]DepartmentofMathematics,PurdueUniversity,WestLafayette,IN47907 [2]DepartmentofMathematics,FudanUniversityShanghai200433,China |
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Abstract: | The solvability of a class of forward-backward stochastic differential equations (SDEs for short) over an arbitrarily prescribed time duration is studied. The authors design a stochastic relaxed control problem, with both drift and difftusion all being controlled, so that the solvability problem is converted to a problem of finding the nodal set of the viscosity solution to a certain Hamilton-Jacobi-Bellman equation. This method overcomes the fatal difficulty encountered in the traditional contraction mapping approach to the existence theorem of such SDEs. |
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Keywords: | Forward-backward stochastic differential equations Stochastic control Relaxed control Viscosity solutions Nodal set |
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