arXiv subjects

Brahim Baadi

Publications and source records attributed to Brahim Baadi.

3 recordsLinked to original sources

arXiv2023

Existence and uniqueness for reflected BSDE with multivariate point process and right upper-semi-continuous obstacle

In a noise driving by a multivariate point process $\mu$ with predictable compensator $\nu$, we prove existence and uniqueness of the reflected backward stochastic differential equation's solution with a lower obstacle $(\xi_{t})_{t\in[0,T]}$ which is assumed to be right upper-semicontinuous but not necessarily right-continuous process and a Lipschitz driver $f$. The result is established by using Mertens decomposition of optional strong (but not necessarily right continuous) super-martingales, an appropriate generalization of It\^{o}'s formula due to Gal'chouk and Lenglart and some tools from optimal stopping theory. A comparison theorem for this type of equations is given.

math.PR↗

arXiv2022

Reflected BSDEs with two completely separated barriers and regulated trajectories in general filtration

In this paper, we study doubly reflected Backward Stochastic Differential Equations defined on probability spaces equipped with filtration satisfying only the usual assumptions of right continuity and completeness in the case where the barriers L and U don't satisfy any regularity assumption (without right continuity). We suppose that the barriers L and U and their left limits are completely separated and we show existence and uniqueness of the solution.

math.PR↗

arXiv2018

Reflected BSDEs when the obstacle is not right-continuous in a general filtration

We prove existence and uniqueness of the reflected backward stochastic differential equation's (RBSDE) solution with a lower obstacle which is assumed to be right upper-semicontinuous but not necessarily right-continuous in a filtration that supports a Brownian motion $W$ and an independent Poisson random measure $π$. The result is established by using some tools from the general theory of processes such as Mertens decomposition of optional strong (but not necessarily right continuous) supermartingales and some tools from optimal stopping theory, as well as an appropriate generalization of Itô's formula due to Gal'chouk and Lenglart. Two applications on dynamic risk measure and on optimal stopping will be given.

math.PR↗