Ever since Bachelier’s PhD thesis in 1900 — a theory of Brownian motion 5 years before Einstein — financial engineering has regrettably outgrown our understanding. The inadequacy of the models used to describe financial markets is often responsible for the worst financial crises, with significant impact on everyday economy. From a physicist’s perspective, understanding price formation in financial markets — namely how markets absorb and process information of thousands of individual agents to come up to a “fair” price — is a truly challenging problem.
We are entering an era where economic and financial data becomes of such quality that scientific theories can be tested at levels of precision comparable to those achieved in natural sciences. We will present some of the most remarkable empirical findings of the past few years, together with some theoretical ideas based on reaction-diffusion models inspired from physics and chemistry.