Anticipated backward stochastic differential equations with jumps under the non-Lipschitz condition

This paper deals with a class of anticipated backward stochastic differential equations with Poisson jumps (ABSDEJs). We first show that there is a duality between anticipated backward stochastic differential equations with jumps and stochastic differential delay equations with jumps (SDDEJs). Then, we prove the existence and uniqueness of adapted solutions and L-P solutions for such ABSDEJs under the non-Lipschitz conditions as well as a comparison theorem is obtained through constructing some iterative equations which are different from iterative equations in Peng and Yang (2009). (C) 2014 Elsevier B.V. All rights reserved.