On Reflection with Two-Sided Jumps

Jarni, Imane; Ouknine, Youssef

doi:10.1007/s10959-020-01024-x

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2020

2025

Publication Types

Select...

Article3

Other1

Relationship

Self Cite1

Independent3

Authors

Journals

Cited by 4 publications

(1 citation statement)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Regarding reflected SDEs driven by optional semimartingales, we quote the work of Jarni and Ouknine [17]. In this work, the authors have extended the reflection problem with jump when the driven process is right continuous left limited, introduced firstly by Chaleyat-Maurel, El Karoui and Marchal in [7], to the case when the driven process has right and left limited trajectories.…”

Section: Introductionmentioning

confidence: 99%

Stochastic differential equations with respect to optional semimartingales and two reflecting regulated barriers

Hilbert¹,

Jarni²,

Ouknine³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

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 deterministic case. Then, we apply our result to study the existence and uniqueness of solutions of reflected stochastic differential equations with respect to optional semimartingales. The study is carried out on a probability space that does not necessarily satisfy the usual conditions.

show abstract

Section: Introductionmentioning

confidence: 99%