关于y单调,关于z一致连续条件下RBSDE的解

Solution of RBSDE with condition of monotonic in y and uniformly continuous in z

为了使反射倒向微分方程在金融和控制领域得到更广泛的应用,通过减弱生成元的条件,在y满足单调性条件、z满足一致连续的条件下,研究单个连续障碍的反射倒向随机微分方程的解的唯一性问题。运用集合论的思想处理反射项,用Lipschitz函数加无穷小项控制一致连续函数的方法处理z解,结合倒向Gronwall不等式得到方程的唯一解。在较弱条件下举出生成元的具体例子。

This paper is aimed at realizing a wider use of RBSDE in finance and control system by relaxing the condition of the generator of RBSDE to investigate the uniqueness problem of RBSDE with one continuous barrier whose generator is monotonic in y and uniformly continuous in z.The method consists of dealing with the reflect component using set theory,dealing with the solution z.Using the Lipschitz function plus a trivial function to controlling the uniformly continuous function,and developing the uniqueness solution of this kind of RBSDE,combined with the Gronwall inequality.The paper gives some concrete examples of this kind of generator.