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A unified approach to well-posedness of type-I backward stochastic Volterra integral equations

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Title: A unified approach to well-posedness of type-I backward stochastic Volterra integral equations
Authors: Hernández, C
Possamaï, D
Item Type: Journal Article
Abstract: 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.
Issue Date: 22-Jun-2021
Date of Acceptance: 22-May-2021
URI: http://hdl.handle.net/10044/1/91794
DOI: 10.1214/21-ejp653
ISSN: 1083-6489
Publisher: Institute of Mathematical Statistics
Start Page: 1
End Page: 35
Journal / Book Title: Electronic Journal of Probability
Volume: 26
Issue: none
Copyright Statement: © 2021 The Author(s). This work is licensed under Creative Commons Attribution 4.0 International License.
Keywords: 0104 Statistics
0105 Mathematical Physics
Statistics & Probability
Publication Status: Published
Open Access location: https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/A-unified-approach-to-well-posedness-of-type-I-backward/10.1214/21-EJP653.full
Online Publication Date: 2021-06-22
Appears in Collections:Financial Mathematics

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