Regularity of BSDEs with a convex constraint on the gains-process

Bruno Bouchard; Romuald Elie; Ludovic Moreau

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arXiv · 1409.5369

Regularity of BSDEs with a convex constraint on the gains-process

Bruno Bouchard·Romuald Elie·Ludovic Moreau

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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.

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BibTeX RIS

Bruno Bouchard, Romuald Elie, Ludovic Moreau. 2014-09-18. Regularity of BSDEs with a convex constraint on the gains-process. https://arxiv.org/abs/1409.5369

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