Scalar BSDEs of iterated-logarithmically sublinear generators with integrable terminal values

TL;DR

This paper proves existence and uniqueness of solutions for scalar backward stochastic differential equations with generators that have iterated-logarithmic continuity, extending previous results to more general cases with integrable terminal values.

Contribution

It introduces a new existence and uniqueness result for scalar BSDEs with iterated-logarithmic continuous generators and integrable terminal conditions, improving prior work.

Findings

Established general existence and uniqueness of solutions.

Extended previous results to iterated-logarithmic continuity.

Applicable to BSDEs with integrable terminal values.

Abstract

We establish a general existence and uniqueness of integrable adapted solutions to scalar backward stochastic differential equations with integrable parameters, where the generator $g$ has an iterated-logarithmic uniform continuity in the second unknown variable $z$. The result improves our previous one in \cite{FanHuTang2023SCL}.