  We consider a stochastic control problem which is composed of a controlled
stochastic differential equation, and whose associated cost functional is
defined through a controlled backward stochastic differential equation. Under
appropriate convexity assumptions on the coefficients of the forward and the
backward equations we prove the existence of an optimal control on a suitable
reference stochastic system. The proof is based on an approximation of the
stochastic control problem by a sequence of control problems with smooth
coefficients, admitting an optimal feedback control. The quadruplet formed by
this optimal feedback control and the associated solution of the forward and
the backward equations is shown to converge in law, at least along a
subsequence. The convexity assumptions on the coefficients then allow to
construct from this limit an admissible control process which, on an
appropriate reference stochastic system, is optimal for our stochastic control
problem.
