论文标题
向后的随机微分方程和向后的随机Volterra积分方程，并带有预期发电机
Backward Stochastic Differential Equations and Backward Stochastic Volterra Integral Equations with Anticipating Generators
论文作者
论文摘要
对于向后的随机微分方程（简称BSDE），当发电机无法逐步测量时，它可能不接受改编的解决方案，这是一个示例所示。但是，对于向后的随机Volterra积分方程（简称BSVIE），允许发电机进行预测。除其他外，这给了BSDE和BSVIE之间的本质区别。在某些适当的条件下，建立了这种BSVIE的良好性。此外，结果扩展到依赖路径的BSVIE，其中发生器可以取决于未知过程的未来路径。另一个发现是，对于路径依赖性的BSVIE，通常无法避免预期发电机的情况，并且与Peng-Yang [22]对预期的BSDES相似的适应性条件不是必需的。
For a backward stochastic differential equation (BSDE, for short), when the generator is not progressively measurable, it might not admit adapted solutions, shown by an example. However, for backward stochastic Volterra integral equations (BSVIEs, for short), the generators are allowed to be anticipating. This gives, among other things, an essential difference between BSDEs and BSVIEs. Under some proper conditions, the well-posedness of such kinds of BSVIEs is established. Further, the results are extended to path-dependent BSVIEs, in which the generators can depend on the future paths of unknown processes. An additional finding is that for path-dependent BSVIEs, in general, the situation of anticipating generators is not avoidable and the adaptedness condition similar to that imposed for anticipated BSDEs by Peng--Yang [22] is not necessary.
