## Bernoulli

• Bernoulli
• Volume 24, Number 3 (2018), 1613-1635.

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

#### 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.

#### Article information

Source
Bernoulli, Volume 24, Number 3 (2018), 1613-1635.

Dates
Revised: June 2015
First available in Project Euclid: 2 February 2018

https://projecteuclid.org/euclid.bj/1517540455

Digital Object Identifier
doi:10.3150/16-BEJ806

Mathematical Reviews number (MathSciNet)
MR3757510

Zentralblatt MATH identifier
06839247

#### Citation

Bouchard, Bruno; Elie, Romuald; Moreau, Ludovic. Regularity of BSDEs with a convex constraint on the gains-process. Bernoulli 24 (2018), no. 3, 1613--1635. doi:10.3150/16-BEJ806. https://projecteuclid.org/euclid.bj/1517540455

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