# BSDEs with mean reflection

@article{Briand2016BSDEsWM, title={BSDEs with mean reflection}, author={P. Briand and R. Elie and Y. Hu}, journal={arXiv: Probability}, year={2016} }

In this paper, we study a new type of BSDE, where the distribution of the Y-component of the solution is required to satisfy an additional constraint, written in terms of the expectation of a loss function. This constraint is imposed at any deterministic time t and is typically weaker than the classical pointwise one associated to reflected BSDEs. Focusing on solutions (Y, Z, K) with deterministic K, we obtain the well-posedness of such equation, in the presence of a natural Skorokhod type… Expand

#### 18 Citations

Quadratic BSDEs with mean reflection

- Mathematics
- 2017

The present paper is devoted to the study of the well-posedness of BSDEs with mean reflection whenever the generator has quadratic growth in the \begin{document}$z$\end{document} argument. This work… Expand

On Z-mean reflected BSDEs

- Mathematics
- 2021

In this paper we provide conditions for the existence of supersolutions to BSDEs with meanreflections on the Z component. We show that, contrary to BSDEs with mean-reflections on the Y component, we… Expand

Mean-field reflected backward stochastic differential equations

- Mathematics
- 2019

In this paper, we study a class of reflected backward stochastic differential equations (BSDEs) of mean-field type, where the mean-field interaction in terms of the distribution of the $Y$-component… Expand

Particles Systems for mean reflected BSDEs

- Mathematics
- 2017

In this paper, we deal with Reflected Backward Stochastic Differential Equations for which the constraint is not on the paths of the solution but on its law as introduced by Briand, Elie and Hu in… Expand

Large Deviations and Exit-times for reflected McKean-Vlasov equations with self-stabilizing terms and superlinear drifts

- Mathematics
- 2020

We study a class of reflected McKean-Vlasov diffusions over a convex domain with self-stabilizing coefficients. This includes coefficients that do not satisfy the classical Wasserstein Lipschitz… Expand

BSDEs with weak reflections and partial hedging of American options

- Mathematics, Economics
- 2017

We introduce a new class of \textit{Backward Stochastic Differential Equations with weak reflections} whose solution $(Y,Z)$ satisfies the weak constraint $\textbf{E}[\Psi(\theta,Y_\theta)] \geq m,$… Expand

Mean reflected stochastic differential equations with jumps

- Mathematics
- Advances in Applied Probability
- 2020

Abstract In this paper, a reflected stochastic differential equation (SDE) with jumps is studied for the case where the constraint acts on the law of the solution rather than on its paths. These… Expand

Dynamic programming equation for the mean field optimal stopping problem

- Mathematics
- 2021

We study the optimal stopping problem of McKean-Vlasov diffusions when the criterion is a function of the law of the stopped process. A remarkable new feature in this setting is that the stopping… Expand

PR ] 2 0 D ec 2 01 7 Particles Systems for Mean Reflected BSDEs

- 2018

In this paper, we deal with Reflected Backward Stochastic Differential Equations for which the constraint is not on the paths of the solution but on its law as introduced by Briand, Elie and Hu in… Expand

Forward and backward stochastic differential equations with normal constraints in law

- Mathematics
- 2020

Abstract In this paper we investigate the well-posedness of backward or forward stochastic differential equations whose law is constrained to live in an a priori given (smooth enough) set and which… Expand

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