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

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.

arXiv comment50 pages

References in corpus (3)

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• Time-Inconsistent Stochastic Optimal Control Problems and Backward Stochastic Volterra Integral Equations
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Cited by in corpus (6)

• Nonlocality, Nonlinearity, and Time Inconsistency in Stochastic Differential Games
• Variation of constants formulae for forward and backward stochastic Volterra integral equations
• Approximations for adapted M-solutions of Type-II backward stochastic Volterra integral equations
• Infinite horizon backward stochastic Volterra integral equations and discounted control problems
• Subgame-perfect equilibrium strategies for time-inconsistent recursive stochastic control problems
• A PDE approach for open-loop equilibriums in time-inconsistent stochastic optimal control problems