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2021 A unified approach to well-posedness of type-I backward stochastic Volterra integral equations
Camilo Hernández, Dylan Possamaï
Author Affiliations +
Electron. J. Probab. 26: 1-35 (2021). DOI: 10.1214/21-EJP653


We study a novel general class of multidimensional type-I backward stochastic Volterra integral equations. Toward this goal, we introduce an infinite family of standard backward SDEs and establish its well-posedness, and we show that it is equivalent to that of a type-I backward stochastic Volterra integral equation. We also establish a representation formula in terms of non-linear semi-linear partial differential equation of Hamilton–Jacobi–Bellman type. As an application, we consider the study of time-inconsistent stochastic control from a game-theoretic point of view. We show the equivalence of two current approaches to this problem from both a probabilistic and an analytic point of view.

Funding Statement

The authors would like to thank Tianxiao Wang and Yushi Hamaguchi for useful comments on a earlier version of this document. The authors gratefully acknowledge the support of the ANR project PACMAN ANR-16-CE05-0027, the PGIF project “Massive entry of renewable energy in Chile: operation, storage and intermittency” and the project “Massive entry of renewable energy: operation, storage and intermittency” funded by the “Make Our Planet Great Again” initiative of the Thomas Jefferson Fund. Camilo Hernández was supported by the CKGSB fellowship.


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Camilo Hernández. Dylan Possamaï. "A unified approach to well-posedness of type-I backward stochastic Volterra integral equations." Electron. J. Probab. 26 1 - 35, 2021.


Received: 8 October 2020; Accepted: 22 May 2021; Published: 2021
First available in Project Euclid: 22 June 2021

Digital Object Identifier: 10.1214/21-EJP653

Primary: 35F21, 35Q93, 93E20


Vol.26 • 2021
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