Financial Modeling in Combinatorics (2024)
Undergraduates: Ajay Misra, Jay Raval, Kishan Gajera, Edgar Perez-Palacios
Faculty Advisor: Ivan Cherednik
Department: Mathematics
This research explores the dynamic interplay between news flow and financial market responses through advanced mathematical modeling. Central to our analysis is the Basic Equation, dN(t)/dt = ctN(t), which postulates that the impact of news on financial markets is directly proportional to the temporal rate of change in news volume. This equation underscores the potent initial impact of news, which diminishes over time. Additionally, we delve into the interaction between news updates and stock prices with two supplementary equations. Equation (3), du(t)/dt = ctu(t) - 1/tp(t), accounts for the cumulative impacts of news and adjustments in stock prices, illustrating that ongoing news coverage has progressively less influence on stock valuations, particularly when stocks are undervalued. Equation (4), dp(t)/dt = atu(t) + bdt*du(t)/dt, connects these dynamics, showing how news directly triggers stock price adjustments. Integrating these foundational equations, our comprehensive model assesses the correlation between news volume, its perceived impact, and subsequent stock price changes. We propose the incorporation of a novel machine learning embedding model to augment the predictiveness of these dynamics. This AI-driven approach aims to leverage deep learning techniques to more accurately predict the impact of news on stock prices, offering valuable insights for investors and market analysts. Our research highlights the potential of combining mathematical rigor with innovative machine learning technologies to advance financial analytics, thereby enhancing investment strategies and promoting market stability through informed, data-driven decision-making.