L´evy 过程驱动的BSDE的反比较定理与Jensen不等式

摘要

本文研究了由一维L´evy过程驱动的倒向随机微分方程（BSDE）的反比较定理。利用一般g -期望下BSDE的反比较定理的证明方法，推导出了一般f -期望下BSDE的反比较定理，并给出了一般f -期望下Jensen不等式成立的充分必要条件。%In this paper, we are devoted to the converse comparison theorem for backward stochastic differential equations (BSDEs, for short) driven by 1-dimensional L´evy processes. With the similar method of the converse comparison theorem under g-expectation, we prove the converse comparison theorem under f-expectation. Moreover, we provide a necessary and sufficient condition for the Jensen’s inequality to hold under the f-expectation, the nonlinear expectation defined by BSDEs driven by L´evy processes.