Mean-field backward stochastic differential equations with conditional reflection

This paper investigated the well-posedness of solutions for a class of mean-field backward stochastic differential equations(BSDEs) with conditional reflection. First, based on the Skorohod lemma, we derived explicit estimates for the solutions and rigorously proved their uniqueness. For the special case where the generator was independent of the solution $(Y,Z)$ and their distribution, we introduced the Snell envelope approach, which not only established the existence of solutions but also revealed their intrinsic connection to optimal stopping problems under partial information. Furthermore, for general generators (dependent on the solution and distribution), we proved the existence of solutions via the contraction mapping arguments. Our work extended the theoretical framework of mean-field BSDEs and provided novel analytical tools for related stochastic control problems.