江蘇省應用數學（中國礦業大學）中心系列學術報告
報告題目：Sub-diffusive Black-Scholes model and Girsanov transform for sub-diffusions
報 告 人：陳振慶 教授 華盛頓大學
報告時間：2025/7/2（周三） 15:30-16:30
報告地點：伟德bvA321
報告摘要：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.
報告人簡介：陳振慶，美國華盛頓大學 (西雅圖) 數學系終身教授，分别于2007年和2014年當選為美國數理統計學會會士和美國數學學會會士。主要從事概率論及随機過程的研究，主要研究方向包括馬爾可夫過程和狄氏空間理論、位勢理論、随機微分方程、擴散過程、穩定過程以及偏微分方程中的概率方法等。現 (曾) 擔任國際著名期刊Potential Analysis的主編以及AOP、AAP、SPA、EJP、JTP、PAMS等期刊編委，2019年榮獲伊藤獎(lto Prize)。出版專著一部，在JEMS、MAMS、Math.Ann.、Adv. Math..CMP、AOP、PTRF、TAMS、JFA等頂尖期刊發表論文近200篇。