A type of time-symmetric forward–backward stochastic differential equations

In this Note, we study a type of time-symmetric forward–backward stochastic differential equations. Under some monotonicity assumptions, we establish the existence and uniqueness theorem by means of a method of continuation. We also give an application. To cite this article: S. Peng, Y. Shi, C. R. Acad. Sci. Paris, Ser. I 336 (2003).