Reflected backward stochastic differential equations driven by a Lévy process. (English) Zbl 1363.60084

Fan, Xiliang; Li, Fang; Zhu, Dongjin

Chin. J. Appl. Probab. Stat. 32, No. 2, 184-200 (2016).

Summary: In this paper, we prove the existence and uniqueness of solutions for reflected backward stochastic differential equations driven by a Lévy process, in which the reflecting barriers are just right continuous with left limits whose jumps are arbitrary. To derive the above results, the monotonic limit theorem of backward stochastic differential equations associated with Lévy process is established.

MSC:

60H15	Stochastic partial differential equations (aspects of stochastic analysis)
60G51	Processes with independent increments; Lévy processes

Keywords:

reflected backward stochastic differential equation; Teugels martingale; penalization method; monotonic limit theorem; Snell envelope