On quadratic multidimensional type-I BSVIEs, infinite families of BSDEs and their applications

This paper investigates multidimensional extended type-I BSVIEs and infinite families of BSDEs in the case of quadratic generators. We establish existence and uniqueness results in the case of fully quadratic as well as Lipschitz-quadratic generators. As a preliminary step, we establish the well-posedness of a class of infinite families of BSDEs, as introduced in Hernandez and Possamai (2021), which are of interest in their own right. Our approach relies on the strategy developed by Tevzadze (2008) for quadratic BSDEs and the treatment of Lipschitz extended type-I BSVIEs in Hernandez and Possamai (2021). We also present and discuss a type of flow property satisfied by this family of BSVIEs. We motivate the analysis of both of these objects by a series of practical applications.& COPY; 2023 Elsevier B.V. All rights reserved.