Integrate-and-fire models of financial markets

This thesis introduces a novel theoretical and computational framework that bridges concepts from physics, complexity science, neuroscience, and behavioural economics to describe financial market dynamics using an integrate-and-fire paradigm. Motivated by the limitations inherent in classical economic theories - especially the efficient market hypothesis and the oversimplification of homogeneous, representative agents- the work explicitly models financial markets as emergent phenomena resulting from the interactions of heterogeneous agents. Traders in this framework integrate information, including market signals and social influences, and decide when decision thresholds are reached, analogous to neuronal firing events. Through computational modelling and systematic analysis, the thesis reveals several significant findings. It demonstrates that neuronal-inspired decision mechanisms, such as inhibition and information decay (reflecting irrationality and limited memory), are critical for replicating widely observed financial phenomena, including speculative bubbles, sudden market crashes, fat-tailed return distributions, and volatility clustering. Further investigations establish clear relationships between hierarchical information structures (information silos), and mispricing, highlighting how network topology profoundly influences market stability and price dynamics. Expanding beyond purely financial applications, the thesis generalises the integrate-and-fire framework into a versatile approach capable of describing broader social dynamics. With this approach, we manage to reproduce wealth distributions of traders in financial markets. Remarkably, this generalised framework also successfully captures complex epidemiological patterns, accurately reproducing real-world data from infectious disease outbreaks, including the COVID-19 pandemic, and capturing features such as secondary infection peaks and intervention effects. Overall, the results underscore the importance of micro-level heterogeneity and network topology in generating complex, non-equilibrium market phenomena, providing new insights into the interplay between individual decision-making and aggregate market behaviour.