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| SOLVABILITY OF FORWARD-BACKWARD SDES AND THE NODAL SET OF HAMILTON-JACOBI-BELLMAN EQUATIONS |
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Citation： |
Ma Jin,Yong Jiongmin.SOLVABILITY OF FORWARD-BACKWARD SDES AND THE NODAL SET OF HAMILTON-JACOBI-BELLMAN EQUATIONS[J].Chinese Annals of Mathematics B,1995,16(3):279~298 |
| Page view： 1345
Net amount： 968 |
Authors： |
Ma Jin; Yong Jiongmin |
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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 diffusion 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. |
Keywords： |
Forward-backward stochastic differential equations,Stochastic control,Relaxed control, Viscosity solutions, Nodal set. |
Classification： |
35K15, 49L20, 49L25, 60H10,
93E20. |
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