Youssef Ouknine
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View article: On Malliavin differentiability and absolute continuity of one-dimensional doubly perturbed diffusion processes
On Malliavin differentiability and absolute continuity of one-dimensional doubly perturbed diffusion processes Open
In this paper, we establish Malliavin differentiability and absolute continuity for $α, β$-doubly perturbed diffusion process with parameters $α<1$ and $β<1$ such that $|ρ| < 1$, where $ ρ: = \frac{αβ}{(1-α)(1-β)}$. Furthermore, under some…
View article: On Carathéodory approximate scheme for a class of one-dimensional doubly perturbed diffusion processes
On Carathéodory approximate scheme for a class of one-dimensional doubly perturbed diffusion processes Open
In this paper, we introduce and study the convergence of new Carathéodory's approximate solution for one-dimensional $α, β$-doubly perturbed stochastic differential equations (DPSDEs) with parameters $α<1$ and $β<1$ such that $|ρ| < 1$, wh…
View article: Reflected Mckean-Vlasov stochastic differential equations with jumps in time-dependent domains
Reflected Mckean-Vlasov stochastic differential equations with jumps in time-dependent domains Open
In this paper, we investigate the deterministic multidimensional Skorokhod problem with normal reflection in a family of time-dependent convex domains that are càdlàg with respect to the Hausdorff metric. We then show the existence and uni…
View article: Intrinsic regularization by noise for $1d$ mean field games
Intrinsic regularization by noise for $1d$ mean field games Open
The purpose of this article is to show that an intrinsic noise with values in the space ${\mathcal P}({\mathbb R})$ of $1d$ probability measures may force uniqueness to first order mean field games. The structure of the noise is inspired f…
View article: Optimal Stopping Under Model Uncertainty in a General Setting
Optimal Stopping Under Model Uncertainty in a General Setting Open
We consider the optimal stopping time problem under model uncertainty $R(v)= {\text{ess}\sup\limits}_{ \mathbb{P} \in \mathcal{P}} {\text{ess}\sup\limits}_{τ\in \mathcal{S}_v} E^\mathbb{P}[Y(τ) \vert \mathcal{F}_v]$, for every stopping tim…
View article: Optimal stopping in predictable setting
Optimal stopping in predictable setting Open
In this study, we delve into the optimal stopping problem by examining the case in which the reward is given by a family $ (\phi(\tau ),\;\;\tau \in {\cal{T}}_0^p) $ of nonnegative random variables indexed by predictable stopping times. We…
View article: Stochastic differential equations with respect to optional semimartingales and two reflecting regulated barriers
Stochastic differential equations with respect to optional semimartingales and two reflecting regulated barriers Open
In this work, we introduce a new Skorokhod problem with two reflecting barriers when the trajectories of the driven process and the barriers are right and left limited. We show that this problem has an explicit unique solution in a determi…
View article: A class of quadratic forward-backward stochastic differential equations
A class of quadratic forward-backward stochastic differential equations Open
We study a class of quadratic forward-backward stochastic differential equations (QFBSDEs) with measurable drift and a continuous generator. We establish some existence and uniqueness results for such QFBSDEs. Our approach is based on a we…
View article: RBSDEs with optional barriers: monotone approximation
RBSDEs with optional barriers: monotone approximation Open
In this short note we consider reflected backward stochastic differential equations (RBSDEs) with a Lipschitz driver and barrier processes that are optional and right lower semicontinuous. In this case, the barrier is represented as a nond…
View article: Reflected and Doubly RBSDEs with Irregular Obstacles and a Large Set of Stopping Strategies
Reflected and Doubly RBSDEs with Irregular Obstacles and a Large Set of Stopping Strategies Open
We introduce a new formulation of reflected BSDEs and doubly reflected BSDEs associated with irregular obstacles. In the first part of the paper, we consider an extension of the classical optimal stopping problem over a larger set of stopp…
View article: Reflected backward stochastic differential equations with optional barriers: monotone approximation
Reflected backward stochastic differential equations with optional barriers: monotone approximation Open
In this short note we consider RBSDE with Lipschitz drivers and barrier processes that are optional and right upper semicontinuous. We treat the case when the barrier can be represented as a decreasing limit of cadlag barriers. We combine …
View article: On the strict value of the non-linear optimal stopping problem
On the strict value of the non-linear optimal stopping problem Open
We address the non-linear strict value problem in the case of a general filtration and a completely irregular pay-off process $(\\xi _{t})$. While the value process $(V_{t})$ of the non-linear problem is only right-uppersemicontinuous, we …
View article: Doubly Reflected BSDEs in the predictable setting
Doubly Reflected BSDEs in the predictable setting Open
In this paper, we introduce a specific kind of doubly reflected Backward Stochastic Differential Equations (in short DRBSDEs), defined on probability spaces equipped with general filtration that is essentially non quasi-left continuous, wh…
View article: On Skorokhod Problem with Two RCLL Reflecting Completely Separated\n Barriers
On Skorokhod Problem with Two RCLL Reflecting Completely Separated\n Barriers Open
In this paper we deal with Skorokhod problem for right continuous left\nlimited (rcll) barriers. We prove existence and uniqueness of the solution when\nthe barriers are only supposed to be rcll and completely separated. Then, we\napply ou…
View article: On Skorokhod Problem with Two RCLL Reflecting Completely Separated Barriers
On Skorokhod Problem with Two RCLL Reflecting Completely Separated Barriers Open
In this paper we deal with Skorokhod problem for right continuous left limited (rcll) barriers. We prove existence and uniqueness of the solution when the barriers are only supposed to be rcll and completely separated. Then, we apply our r…
View article: Optimal Stopping in General Predictable Framework
Optimal Stopping in General Predictable Framework Open
In this paper, we study the optimal stopping problem in the case where the reward is given by a family $(ϕ(τ),\;\;τ\in \stopo)$ of non negative random variables indexed by predictable stopping times. We treat the problem by means of Snell'…
View article: Non linear optimal stopping problem and Reflected BSDEs in the predictable setting
Non linear optimal stopping problem and Reflected BSDEs in the predictable setting Open
In the first part of this paper, we study RBSDEs in the case where the filtration is not quasi-left continuous and the lower obstacle is given by a predictable process. We prove the existence and uniqueness by using some results of optimal…
View article: Doubly Reflected BSDEs and ${\cal E}^{f}$-Dynkin games: beyond the right-continuous case
Doubly Reflected BSDEs and ${\cal E}^{f}$-Dynkin games: beyond the right-continuous case Open
We formulate a notion of doubly reflected BSDE in the case where the barriers $\xi$ and $\zeta$ do not satisfy any regularity assumption and with a general filtration. Under a technical assumption (a Mokobodzki-type condition), we show exi…
View article: Doubly Reflected BSDEs and $\mathcal{E} ^{{f}}$-Dynkin games: beyond the right-continuous case
Doubly Reflected BSDEs and $\mathcal{E} ^{{f}}$-Dynkin games: beyond the right-continuous case Open
Grigorova M, Imkeller P, Quenez M-C, Ouknine Y. Doubly Reflected BSDEs and $\\mathcal{E}$$^ƒ$-Dynkin games: beyond the right-continuous case. Center for Mathematical Economics Working Papers. Vol 598. Bielefeld: Center for Mathematical Eco…
View article: Pathwise uniqueness of non-uniformly elliptic SDEs with rough\n coefficients
Pathwise uniqueness of non-uniformly elliptic SDEs with rough\n coefficients Open
In this paper we review and improve pathwise uniqueness results for some\ntypes of one-dimensional stochastic differential equations (SDE) involving the\nlocal time of the unknown process. The diffusion coefficient of the SDEs we\nconsider…