The solvability of a class of forward-backward stochastic differential differential equations(SDEs for short)over an arbitrarily prescribed time duration is studied. The authors design a stochastic relaxed control pro...The solvability of a class of forward-backward stochastic differential 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.展开更多
文摘The solvability of a class of forward-backward stochastic differential 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.
