BSDE Associated With Levy Processes And Completion Of A Levy Market With Power-Jump Assets

In this paper, we prove the existence and uniqueness of the adapted solution of backwardstochastic differential equations (BSDEs in short) driven by Teugels martingales and anindependent Brownian motion by using predictable representation theorem and the fixed pointtheorem about contract mapping, and give the comparison theory of BSDE driven by Levyprocesses. Next we study the existence and uniqueness of this kind of equations under localLipschitz condition. Then we prove the existence and uniqueness of FBSDE, in which theforward is It(?)'s stochastic differential equation, the backward is stochastic differentialequation driven by Teugels martingales and an independent Brownian motion. At last, weenlarge the market by series of very special assets (power-jump assets) related to thepower-jump processes of the underlying Levy process. By using the predictable representationproperty and the theorem of completion, we prove that the market can be completed.