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

Camilo Hernández

Stochastic Processes and their Applications, 2023, vol. 162, issue C, 249-298

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 generators. As a preliminary step, we establish the well-posedness of a class of infinite families of BSDEs, as introduced in Hernández and Possamaï (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 Hernández and Possamaï (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.

Keywords: Backward stochastic Volterra integral equations; Representation of partial differential equations; Infinite families of BSDEs; Backward stochastic differential equations; Risk-sensitive nonzero sum games; Time inconsistency. (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:162:y:2023:i:c:p:249-298

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DOI: 10.1016/j.spa.2023.05.001

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