# American Institute of Mathematical Sciences

June  2021, 11(2): 433-478. doi: 10.3934/mcrf.2020043

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

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

Received  April 2020 Revised  August 2020 Published  October 2020

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.

Citation: Yushi Hamaguchi. Extended backward stochastic Volterra integral equations and their applications to time-Inconsistent stochastic recursive control problems. Mathematical Control & Related Fields, 2021, 11 (2) : 433-478. doi: 10.3934/mcrf.2020043
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