Economics has long drawn inspiration from the physical sciences. In the nineteenth century, economists such as Léon Walras described economies as systems of interacting markets moving towards equilibrium. Finance later introduced probability into this picture. In 1900, Louis Bachelier modelled price movements as random processes, laying early foundations for mathematical finance and, eventually, models such as Black–Scholes.
Real markets, however, rarely behave as neatly as these early frameworks assume. Benoît Mandelbrot showed that extreme price movements occur more frequently than a normal distribution predicts, while periods of high and low volatility tend to cluster. Herbert Simon and Thomas Schelling further demonstrated that individuals operate with limited information and that simple local decisions can produce unexpected collective outcomes. These ideas helped give rise to complexity economics: the study of economies and markets as evolving systems of interacting, adaptive participants rather than as systems that remain permanently close to equilibrium.
Students at FARII approach these questions using ideas from economics, physics, mathematics, statistics, and computer science. Concepts such as fluctuations, phase transitions, networks, feedback, stochastic processes, and information theory provide tools for studying how markets move between periods of stability, uncertainty, and crisis.
Our current work focuses on identifying market regimes, modelling volatility and extreme events, and understanding how information and participant behaviour affect financial systems. Students investigate how statistical models, machine-learning methods, and agent-based simulations can be used to detect changing market conditions and explain phenomena such as herding, bubbles, liquidity shocks, and crashes.
These ideas also inform the development of adaptive trading and risk-management models. Rather than assuming that one strategy will work under all conditions, our models examine how decisions should change across different volatility and market regimes. Students study not only whether a model performs well, but also how reliable it is, how it responds to uncertainty, and how it behaves when the market enters conditions unlike those seen during training.
Economics and Complexity Theory therefore asks a broader question than how prices move: how do individual decisions, information, institutions, and external events combine to produce the behaviour of an entire financial system? By turning these questions into models that can be simulated, tested, and improved, students learn to study markets as dynamic and interconnected systems.