Weak solutions of backward stochastic differential equations with continuous generator

Abstract

This paper provides a simple approach for the consideration of quadratic BSDEs with bounded terminal We prove the existence of a weak solution to a backward stochastic differential equation (BSDE)in a finite-dimensional space, where f (t, x, y, z) is affine with respect to z, and satisfies a sublinear growth condition and a continuity condition. This solution takes the form of a triplet (Y, Z, L) of processes defined on an extended probability space and satisfyingwhere L is a martingale with possible jumps which is orthogonal to W . The solution is constructed on an extended probability space, using Young measures on the space of trajectories. One component of this space is the Skorokhod space D endowed with the topology S of Jakubowski.