A unified approach to well-posedness of type-I backward stochastic Volterra integral equations
Open access
Date
2021Type
- 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. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000498813Publication status
publishedExternal links
Journal / series
Electronic Journal of ProbabilityVolume
Pages / Article No.
Publisher
University of WashingtonSubject
Backward stochastic Volterra integral equations; consistent planning; equilibrium Hamilton–Jacobi–Bellman equation; representation of partial differential equations; Time inconsistencyOrganisational unit
09728 - Possamaï, Dylan / Possamaï, Dylan
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