  This paper is concerned with the existence of optimal controls for backward
stochastic partial differential equations with random coefficients, in which
the control systems are represented in an abstract evolution form, i.e.
backward stochastic evolution equations. Under some growth and monotonicity
conditions on the coefficients and suitable assumptions on the Hamiltonian
function, the existence of the optimal control boils down to proving the
uniqueness and existence of a solution to the stochastic Hamiltonian system,
i.e. a fully coupled forward-backward stochastic evolution equation. Using some
a prior estimates, we prove the uniqueness and existence via the method of
continuation. Two examples of linear-quadratic control are solved to
demonstrate our results.
