Title:From Black-Scholes Equation to James Simmons' Renaissance Technologies,Entropy and the Driving Energy
Speaker:Xiaolin Li, Stony Brook University
Time:2025.10.21 16:00-17:00
Location:新楼308
Abstract:
Fischer Black, Myron Scholes, and Robert Merton developed the Black-Scholes model for option pricing—a groundbreaking contribution that earned Scholes and Merton the Nobel Prize in Economics in 1997. The model is built on the assumption that stock prices follow a log-normal Markov process, with the risk-free interest rate acting as the drift term. However, the work of James Simons and his firm, Renaissance Technologies, has demonstrated that certain minority market behaviors exhibit a degree of statistical predictability. In this talk, I present my own study on this topic. I will trace the development from the binomial options pricing model to the Black-Scholes equation, highlighting the mathematical and financial significance of its solution. I will then introduce a set of low-entropy market groups that deviate from the standard Markovian assumptions, and explain how these anomalies can be exploited in stock trading and portfolio optimization. Finally, I will show how computational learning techniques can be used to detect and capitalize on these non-random patterns.