We introduce a class of one-dimensional continuous reflected backward stochastic Volterra integral equations driven by Brownian motion, where the reflection keeps the solution above a given stochastic process (lower obstacle). We prove existence and uniqueness by a fixed point argument and derive a comparison result. Moreover, we show how the solution of our problem is related to a time-inconsistent optimal stopping problem and derive an optimal strategy.

中文翻译：

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一类反射后向随机Volterra积分方程及相关的时间不一致最优停止问题

我们引入了一类由布朗运动驱动的一维连续反射后向随机沃尔泰拉积分方程，其中反射使解保持在给定的随机过程（下障碍）之上。我们通过不动点论证证明存在唯一性，并得出比较结果。此外，我们展示了我们问题的解决方案如何与时间不一致的最优停止问题相关，并推导出最优策略。