勷勤数学•专家报告

题      目：Recent progress about sub-diffusion process

报  告  人： 张帅琪 教授  (邀请人：杨舟)

                                    中国矿业大学

时      间： 6月5日  11：00-12:00

地     点：数科院西楼二楼会议室

报告人简介:

       中国矿业大学数学学院教授，博士生导师，矿大“攀登学者A类”，前广东工业大学“青年百人”。中国数学会数学控制论及其应用专委会委员，中国工业与应用数学学会金融数学与精算保险专业委员会委员，中国工业与应用数学学会智能控制与博弈专业委员会委员。2012年于中南大学博士毕业，澳门大学博士后，新加坡国立大学博士后。从事随机分析，随机控制，非线性滤波，数理金融的研究。在控制领域三大顶刊之一SIAM Journal on Control and Optimization, 概率权威刊物 Stochastic Processes and their Applications，  方程领域权威刊物 Journal of Differential Equations,  精算领域权威刊物 Scandinavian Actuarial Journal,  中国科学：数学 等刊物发表论文。主持国家自然科学基金面上项目、青年项目、天元基金项目，教育部人文社科基金规划基金项目，江苏省自然科学基金面上项目，河北省自然科学基金青年基金等。出版国家“十四五”重点出版物、现代数学基础丛书第201册《随机分析与控制简明教程》

摘      要：

       In this talk, we show our recent research about the systems driven by sub-diffusion B_{L_t}. Here B is a Brownian motion on R and L_t:=inf{r > 0 : S_r > t}, t ≥ 0, is the inverse of a subordinator S with drift κ > 0 that is independent of B. The martingale representation theorem is established. Based on this, the existence and uniqueness of backward stochastic differential equations, and further forward and backward stochastic differential equations driven by B_{L_t} is proved. Furthermore, L^p theorem is alsostudied. Then, the control problem for the system driven by anomalous sub-diffusion is investigated, which have nontrivial mixed features of deterministic and stochastic controls. We also investigate the European option pricing problem under this sub-diffusive Black-Scholes model. For this, we prove the Girsanov transform for sub-diffusions and use it to find risk-neutral probability measures for the new Black-Scholes model. At last, filtering under sub-diffusion framework is established.

          欢迎老师、同学们参加、交流！