MINIMAL SUPERSOLUTION OF BSDES DRIVEN BY CONTINUOUS MARTINGALES IN A GENERAL FILTRATION

Authors

Badr Elmansouri, Cadi Ayyad University (UCA), National School of Applied Sciences of Marrakech (ENSA-M), BP 575, Avenue Abdelkrim Khattabi, 40000, Guéliz, Marrakech, MoroccoFollow
Mohamed El Otmani, Laboratory of Analysis and Applied Mathematics (LAMA), Faculty of Sciences Agadir, Ibn Zohr University, 80000, Agadir, MoroccoFollow

Abstract

In this paper, we study minimal supersolutions of backward stochastic differential equations (BSDEs) driven by a continuous local martingale in a general filtration. We establish existence, uniqueness, and stability results under various mild conditions on the terminal value and the generator. Additionally, we explore the connection between the concept of non-linear expectation and minimal supersolutions, emphasizing the specific properties that are relevant to our framework. We also prove a general monotonic limit theorem and apply this result to determine the smallest constrained supersolution of a BSDE with a possibly non-convex constraint.

Recommended Citation

Elmansouri, Badr and El Otmani, Mohamed (2025) "MINIMAL SUPERSOLUTION OF BSDES DRIVEN BY CONTINUOUS MARTINGALES IN A GENERAL FILTRATION," Journal of Stochastic Analysis: Vol. 6: No. 3, Article 3.
DOI: 10.31390/josa.6.3.03
Available at: https://repository.lsu.edu/josa/vol6/iss3/3

DOI

10.31390/josa.6.3.03