  In this paper we show the existence and form uniqueness of a solution for
multidimensional backward stochastic differential equations driven by a
multidimensional L\'{e}vy process with moments of all orders. The results are
important from a pure mathematical point of view as well as in the world of
finance: an application to Clark-Ocone and Feynman-Kac formulas for
multidimensional L\'{e}vy processes is presented. Moreover, the Feynman-Kac
formula and the related partial differential integral equations provide an
analogue of the famous Black-Scholes partial differential equation and thus can
be used for the purpose of option pricing in a multidimensional L\'{e}vy
market.
