  The paper is concerned with optimal control of backward stochastic
differential equation (BSDE) driven by Teugel's martingales and an independent
multi-dimensional Brownian motion, where Teugel's martingales are a family of
pairwise strongly orthonormal martingales associated with L\'{e}vy processes
(see Nualart and Schoutens \cite{NuSc}). We derive the necessary and sufficient
conditions for the existence of the optimal control by means of convex
variation methods and duality techniques. As an application, the optimal
control problem of linear backward stochastic differential equation with a
quadratic cost criteria (called backward linear-quadratic problem, or BLQ
problem for short) is discussed and characterized by stochastic Hamilton
system.
