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

作者：Tu, Shuheng; Hao, Wu^*

来源：Statistics & Probability Letters, 2014, 92: 215-225.

DOI：10.1016/j.spl.2014.06.001

• BSDE
• Non-Lipschitz
• Comparison
• Anticipated
• Jumps

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).

• 出版日期2014-9
• 单位中南民族大学; 华中科技大学