We study the existence and uniqueness of the solution to a forward-backward stochastic differential equation with subdifferential operator in the backward equation. This kind of equations includes, as a particular cas...We study the existence and uniqueness of the solution to a forward-backward stochastic differential equation with subdifferential operator in the backward equation. This kind of equations includes, as a particular case, multi-dimensional forward-backward stochastic differential equation where the backward equation is reflected on the boundary of a closed convex(time-independent) domain. Moreover, we give a probabilistic interpretation for the viscosity solution of a kind of quasilinear variational inequalities.展开更多
基金supported by Australian Research Council’s Discovery Projects Funding Scheme(Grant No.DP120100895)
文摘We study the existence and uniqueness of the solution to a forward-backward stochastic differential equation with subdifferential operator in the backward equation. This kind of equations includes, as a particular case, multi-dimensional forward-backward stochastic differential equation where the backward equation is reflected on the boundary of a closed convex(time-independent) domain. Moreover, we give a probabilistic interpretation for the viscosity solution of a kind of quasilinear variational inequalities.