Communications in Information and Systems

Volume 21 (2021)

Number 4

BMO martingale method for backward stochastic differential equations driven by general càdlàg local martingales

Pages: 561 – 589

DOI: https://dx.doi.org/10.4310/CIS.2021.v21.n4.a3

Authors

Yunzhang Li (Department of Finance and Control Sciences, School of Mathematical Sciences, Fudan University, Shanghai, China)

Shanjian Tang (Department of Finance and Control Sciences, School of Mathematical Sciences, Fudan University, Shanghai, China)

Abstract

In this paper we study time-discontinuous nonlinear multi-dimensional backward stochastic differential equations (BSDEs) driven by general càdlàg local martingales. The Lipschitz coefficients of the generators are allowed to be unbounded. The time-discontinuous BMO martingale theory, in particular Fefferman’s inequality, is used to study the existence and uniqueness of solution in $\mathcal{S}^p$ with $p \in (1, \infty]$.

Keywords

backward stochastic differential equations, càdlàg local martingale, time-discontinuous BMO martingale theory, Fefferman’s inequality

Full Text (PDF format)

The research of Y. Li was supported by China National Postdoctoral Program for Innovative Talents (Grant No. BX20200096).

The research of S. Tang was supported by National Natural Science Foundation of China (Grant No. 11631004).

Received 12 May 2020

Published 4 June 2021