  Motivated from time-inconsistent stochastic control problems, we introduce a
new type of coupled forward-backward stochastic systems, namely, flows of
forward-backward stochastic differential equations. They are systems consisting
of a single forward SDE and a continuum of BSDEs, which are defined on
different time-intervals and connected via an equilibrium condition. We
formulate a notion of equilibrium solutions in a general framework and prove
small-time well-posedness of the equations. We also consider discretized flows
and show that their equilibrium solutions approximate the original one,
together with an estimate of the convergence rate.
