Extended backward stochastic Volterra integral equations and their applications to time-Inconsistent stochastic recursive control problems

Yushi Hamaguchi

doi:10.3934/mcrf.2020043

Article Contents

2021, Volume 11, Issue 2: 433-478. Doi: 10.3934/mcrf.2020043

This issue Previous Article Stable determination of a vector field in a non-Self-Adjoint dynamical Schrödinger equation on Riemannian manifolds Next Article

Extended backward stochastic Volterra integral equations and their applications to time-Inconsistent stochastic recursive control problems

Yushi Hamaguchi

Department of Mathematics, Kyoto University, Kyoto 606–8502, Japan

Received: March 31, 2020

Revised: July 31, 2020

Early access: October 2020

Published: June 2021

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Abstract

In this paper, we study extended backward stochastic Volterra integral equations (EBSVIEs, for short). We establish the well-posedness under weaker assumptions than the literature, and prove a new kind of regularity property for the solutions. As an application, we investigate, in the open-loop framework, a time-inconsistent stochastic recursive control problem where the cost functional is defined by the solution to a backward stochastic Volterra integral equation (BSVIE, for short). We show that the corresponding adjoint equations become EBSVIEs, and provide a necessary and sufficient condition for an open-loop equilibrium control via variational methods.

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Mathematics Subject Classification: Primary: 93E20, 60H20; Secondary: 49K45, 47J30.

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