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.

中文翻译：

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扩展后向随机Volterra积分方程及其在时间不一致的随机递归控制问题中的应用

在本文中，我们研究了扩展的后向随机Volterra积分方程（简称EBSVIE）。我们在比文献更弱的假设下建立了适定性，并证明了该解的一种新的正则性质。作为一种应用，我们在开环框架中研究了时间不一致的随机递归控制问题，其中成本函数由向后随机Volterra积分方程（简称BSVIE）的解定义。我们表明，相应的伴随方程成为EBSVIE，并通过变分方法为开环平衡控制提供了充要条件。