Minimal supersolutions of BSDEs with lower semicontinuous generators

Abstract

We study minimal supersolutions of backward stochastic differential equations. We show the existence and uniqueness of the minimal supersolution, if the generator is jointly lower semicontinuous, bounded from below by an affine function of the control variable, and satisfies a specific normalization property. Semimartingale convergence is used to establish the main result. © Association des Publications de l'Institut Henri Poincaré, 2014.