Brown运动和时间变换的Lévy噪声驱动的BSDEs解的存在唯一性及应用

非线性倒向随机微分方程（简称BSDE）由我国著名数学家彭实戈院士及其合作者于1990年提出并迅速发展为随机分析与金融数学研究领域的核心和热点问题之一，引起人们高度关注与研究。本项目旨在以随机分析与现代概率论为基础，深入地研究弱单调条件下超前BSDE Lp(p≥1)解和时间变换的Lévy噪声驱动的BSDE Lp(p≥2)解的存在唯一性和稳定性；建立时间变换Lévy噪声驱动的BSDE的生成元表示定理，揭示生成元与对过程的动态凸（一致）风险度量的等价关系。所得结果将推广和完善已有的相关结果，推动BSDE理论的进一步发展。

Nonlinear backward stochastic differential equation (short for BSDE) that was proposed by academician Shige Peng who is a famous mathematician in China and his collaborators in 1990 has rapidly developed into one of the core and hot issues in the field of stochastic analysis and financial mathematics. Based on the stochastic analysis and modern probability theory, the purpose of this project is to deeply study the existence, uniqueness and stability of Lp(p≥1) solutions for anticipated BSDE and Lp(p≥2) solutions for BSDE driven by time-change Lévy noise under weakly monotone conditions. For BSDE driven by time-change Lévy noise, the generator representation theorem has been established, and the equivalent relationship between its generator and dynamic convex (consistent) risk measure of process has been revealed. The obtained results will extend and improve the existing results and promote the further development of BSDE theory.