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

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

Type
Article accepté pour publication ou publié
External document link
https://arxiv.org/abs/1409.5369v1
Date
2018
Journal name
Bernoulli
Volume
24
Number
3
Publisher
International Statistical Institute
Published in
Paris
Pages
1613-1635
Publication identifier
10.3150/16-BEJ806
Metadata
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Author(s)
Bouchard, Bruno
Elie, Romuald
Moreau, Ludovic
Abstract (EN)
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-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.
Subjects / Keywords
Backward stochastic differential equation with a constraint; stability; regularity

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