1. On quadratic multidimensional type-I BSVIEs, infinite families of BSDEs and their applications
- Author
-
Hern��ndez, Camilo
- Subjects
Statistics and Probability ,Optimization and Control (math.OC) ,Applied Mathematics ,Modeling and Simulation ,Probability (math.PR) ,FOS: Mathematics ,Mathematics - Optimization and Control ,Mathematics - Probability ,60H20, 35K58, 60H30 - Abstract
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 quadratic generators. We also present and discuss a type of flow property satisfied by this family of BSVIEs. As a preliminary step, we establish the well-posedness of a class of infinite families of BSDEs, as introduced in Hern{\aa}ndez and Possama\"i [20], which are of interest in their own right. Our approach relies on the strategy developed by Tevsadze [49] for quadratic BSDEs and the treatment of Lipschitz extended type-I BSVIEs in [20]. We motivate their analysis of both of these objects by a series of practical applications.
- Published
- 2023