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 $\frac{1}{2}$-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.
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. https://doi.org/10.3150/16-BEJ806
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