江苏省应用数学（中国矿业大学）中心系列学术报告
报告题目：Sub-diffusive Black-Scholes model and Girsanov transform for sub-diffusions
报 告 人：陈振庆 教授 华盛顿大学
报告时间：2025/7/2（周三） 15:30-16:30
报告地点：数学学院A321
报告摘要：We propose a novel Black-Scholes model under which the stock price processes are modeled by stochastic differential equations driven by a sub-diffusion. The new framework can capture the less financial activity phenomenon during the bear markets while having the classical Black-Scholes model as its special case. The sub-diffusive spot market is arbitrage-free but is in general incomplete. We investigate the pricing for European-style contingent claims under this new model. For this, we study Girsanov transform for sub-diffusions and use it to find risk-neutral probability measure for the new Black-Scholes model. Finally, we derive the explicit formula for the price of European call options and show that it can be determined by a partial differential equation involving fractional derivative in time, which we coin a time-fractional Black-Scholes PDE. Based on a joint work with Shuaiqi Zhang.
报告人简介：陈振庆，美国华盛顿大学 (西雅图) 数学系终身教授，分别于2007年和2014年当选为美国数理统计学会会士和美国数学学会会士。主要从事概率论及随机过程的研究，主要研究方向包括马尔可夫过程和狄氏空间理论、位势理论、随机微分方程、扩散过程、稳定过程以及偏微分方程中的概率方法等。现 (曾) 担任国际著名期刊Potential Analysis的主编以及AOP、AAP、SPA、EJP、JTP、PAMS等期刊编委，2019年荣获伊藤奖(lto Prize)。出版专著一部，在JEMS、MAMS、Math.Ann.、Adv. Math..CMP、AOP、PTRF、TAMS、JFA等顶尖期刊发表论文近200篇。