Backward stochastic Volterra integral equations with time delayed generators

In this paper, we study backward stochastic Volterra integral equations of type‐I with time delayed generators. We derive an existence and uniqueness result under a small time horizon or a small Lipschitz constant. We provide with two example that this condition is necessary. However, this equation has a unique solution for arbitrary time horizon and Lipschitz constant. Finally, with additive assumptions, we derive a path continuity property.