A comonotonic theorem for BSDEs

Pardoux and Peng (Systems Control Lett. 14 (1990) 55) introduced a class of nonlinear backward stochastic differential equations (BSDEs). According to Pardoux and Pengʹs theorem, the solution of this type of BSDE consists of a pair of adapted processes, say ( y , z ) . Since then, many researchers have been exploring the properties of this pair solution ( y , z ) , especially the properties of the first part y. In this paper, we shall explore the properties of the second part z . A comonotonic theorem with respect to z is obtained. As an application of this theorem, we prove an integral representation theorem of the solution of BSDEs.