论文标题
延伸后的随机伏尔泰式积分方程及其在时间矛盾的随机递归控制问题上的应用
Extended backward stochastic Volterra integral equations and their applications to time-inconsistent stochastic recursive control problems
论文作者
论文摘要
在本文中，我们研究了向后扩展的随机燃烧器积分方程（简称EBSVIE）。我们在弱的假设下建立了良好的性质，而不是文献，并证明了解决方案的一种新型规律性。作为应用程序，我们在开环框架中调查了一个时间不一致的随机递归控制问题，其中成本函数由向后的随机伏尔泰拉积分方程（简称BSVIE）定义。我们表明，相应的伴随方程成为EBSVIE，并通过变异方法为开环平衡控制提供了必要和足够的条件。
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.
