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
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1409.5369v1
International Statistical Institute
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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 / KeywordsBackward stochastic differential equation with a constraint; stability; regularity
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