Skip to main content
User Image

Mhamed Eddahbi

Professor

Faculty

كلية العلوم
Department of Mathematics, College of Sciences, King Saud University, Building 4, second floor, Office Nu. 2B65, PO. Box 2455 Riyadh, Z.C. 11451
publication
Journal Article
2024

One-Dimensional BSDEs with Jumps and Logarithmic Growth

In this study, we explore backward stochastic differential equations driven by a Poisson process and an independent Brownian motion, denoted for short as BSDEJs. The generator exhibits logarithmic growth in both the state variable and the Brownian component while maintaining Lipschitz continuity with respect to the jump component. Our study rigorously establishes the existence and uniqueness of solutions within suitable functional spaces. Additionally, we relax the Lipschitz condition on the Poisson component, permitting the generator to exhibit logarithmic growth with respect to all variables. Taking a step further, we employ an exponential transformation to establish an equivalence between a solution of a BSDEJ exhibiting quadratic growth in the $z$-variable  and a BSDEJ showing a logarithmic growth with respect to $y$ and $z$.

Publisher Name
Axioms
Publishing City
Switzerland
Volume Number
13
Issue Number
6, 354
Pages
1-31
more of publication
publications

In this paper, we considered a stochastic model of chemical reactive flows acting through porous media under the influence of nonlinear external random fluctuations, where the interchanges of…

by Mhamed Eddahbi, Mogtaba Mohammed, and Hammou El-Otmany
2024
Published in:
AIMS Mathematics
publications

In this study, we explore backward stochastic differential equations driven by a Poisson process and an independent Brownian motion, denoted for short as BSDEJs. The generator exhibits logarithmic…

by E. M. B. Bouhadjar, N. Khelfallah, M.Eddahbi
2024
Published in:
Axioms
publications

The predominant approach for studying volatility is through various GARCH specifications, which are widely utilized in model-based analyses. This study focuses on assessing the predictive…

by B. Benaid, I. Al Hasani, M. Eddahbi
2024
Published in:
Symmetry