Scalar BSDEs of iterated-logarithmically sub-linear generators with integrable terminal values

Abstract

We establish a general existence and uniqueness result of integrable adapted solutions to scalar backward stochastic differential equations with integrable parameters, where the generator g has an iterated-logarithmically uniform continuity in the second unknown variable z. The result improves our previous one in Fan et al. (2023), and can be applied to the (conditional) g-expectation and the star-shaped risk measure.