👉 Cardiff mathematics, also known as the "Cardiff model," is a stochastic process used to describe the evolution of a population of interacting agents, particularly in the context of financial markets and biological systems. It was developed by mathematicians at the University of Cardiff, notably Andrew Barnett and his colleagues, to model the dynamics of a large number of traders or agents making decisions based on incomplete information. The core idea is to represent each agent's state as a probability distribution over possible outcomes, and the evolution of these distributions is governed by a set of stochastic differential equations (SDEs). These SDEs incorporate both deterministic trends and random fluctuations, allowing for the modeling of complex behaviors such as herding, volatility clustering, and market crashes. The model is particularly useful for understanding phenomena like price movements, liquidity dynamics, and the emergence of market regimes. By using a combination of probability theory, stochastic calculus, and numerical methods, Cardiff mathematics provides a flexible framework for analyzing and simulating the intricate interactions within financial systems.
