L^p solutions of anticipated backward stochastic differential equations under monotonicity and general increasing conditions

Abstract

In this paper, we deal with a class of anticipated backward stochastic differential equations (anticipated BSDEs) under weak assumptions on the coefficients. We prove the existence and uniqueness result for solutions of anticipated BSDEs under monotonicity and general increasing conditions on , with Lipschitz on . Furthermore, we give several comparison theorems with respect to 1-dimensional anticipated BSDEs.

Keywords::

• anticipated backward stochastic differential equation (anticipated BSDE)
• monotonicity condition
• comparison theorem

Keywords::

• Primary 60H10

Acknowledgement

The authors would like to thank the anonymous referee for his/her constructive suggestions and valuable comments that greatly improved this paper. The work of Feng Hu is supported by the National Natural Science Foundation of China (No. 11301295), the Program for Scientific Research Innovation Team in Colleges and Universities of Shandong Province of China and the Program for Scientific Research Innovation Team in Applied Probability and Statistics of Qufu Normal University (No. 0230518). The work of Zengjing Chen is supported by the National Natural Science Foundation of China (Nos. 11231005 and 11171062).

Disclosure statement

No potential conflict of interest was reported by the authors.