Regularity of BSDEs with a convex constraint on the gains-process
Abstract
We consider the minimal super-solution of a backward stochastic differential equation with constraint on the gains-process. The terminal condition is given by a function of the terminal value of a forward stochastic differential equation. Under boundedness assumptions on the coefficients, we show that the first component of the solution is Lipschitz in space and 1/2-H\"older in time with respect to the initial data of the forward process. Its path is continuous before the time horizon at which its left-limit is given by a face-lifted version of its natural boundary condition. This first component is actually equal to its own face-lift. We only use probabilistic arguments. In particular, our results can be extended to certain non-Markovian settings.
Keywords
Cite
@article{arxiv.1409.5369,
title = {Regularity of BSDEs with a convex constraint on the gains-process},
author = {Bruno Bouchard and Romuald Elie and Ludovic Moreau},
journal= {arXiv preprint arXiv:1409.5369},
year = {2014}
}