Singular Mean-Field Backward Stochastic Volterra Integral Equations in Infinite Dimensional Spaces [Conference Object]

Abstract

In the current study, we investigate singular mean-field backward stochastic Volterra integral equations (MF-BSVIEs) within the framework of infinite-dimensional spaces. Initially, we establish the well-posedness of singular MF-BSVIEs under appropriate assumptions, rigorously analyzing the conditions necessary for existence and uniqueness of solutions. Subsequently, we extend our analysis to examine the well-posedness of singular mean-field forward stochastic Volterra integral equations (MF-FSVIEs), again under suitable theoretical conditions. Finally, we apply our findings by formulating the Pontryagin maximum principle, thereby demonstrating the practical implications and applications of our theoretical results. © 2025 IEEE.