Open Access
August 2018 Regularity of BSDEs with a convex constraint on the gains-process
Bruno Bouchard, Romuald Elie, Ludovic Moreau
Bernoulli 24(3): 1613-1635 (August 2018). DOI: 10.3150/16-BEJ806


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 $\frac{1}{2}$-Hölder 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.


Download Citation

Bruno Bouchard. Romuald Elie. Ludovic Moreau. "Regularity of BSDEs with a convex constraint on the gains-process." Bernoulli 24 (3) 1613 - 1635, August 2018.


Received: 1 September 2014; Revised: 1 June 2015; Published: August 2018
First available in Project Euclid: 2 February 2018

zbMATH: 06839247
MathSciNet: MR3757510
Digital Object Identifier: 10.3150/16-BEJ806

Keywords: backward stochastic differential equation with a constraint , regularity , stability

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 3 • August 2018
Back to Top