The problem of stock market mathematics and Mandelbrot’s bottom-up approach

In this paper, I explore the efforts to mathematize finance—particularly stock markets—and analyze what is gained and lost through this process, focusing on Mandelbrot’s mathematical theory. I specifically investigate two main approaches to building a mathematical framework for financial systems: the top-down and bottom-up approaches, assessing the epistemic and methodological benefits and drawbacks of each. I argue that Mandelbrot’s theory aligns with the bottom-up approach, and I will compare it to another attempt to mathematize stock markets: Sornette’s econophysical approach, which follows a top-down methodology. These two cases offer valuable insights into the creation of scientific theories and the process of mathematizing complex phenomena like stock markets.