Statistical finance

Statistical finance, is the application of econophysics to financial markets. Instead of the normative roots of much of the field of finance, it uses a positivist framework including exemplars from statistical physics with an emphasis on emergent or collective properties of financial markets. The starting point for this approach to understanding financial markets are the empirically observed stylized facts.

Statistical finance is focused on three areas:

It is noteworthy that financial econometrics also has a focus on the first two of these three areas. However, there is almost no overlap or interaction between the community of statistical finance researchers (who typically publish in physics journals) and the community of financial econometrics researchers (who typically publish in economics journals).

Behavioural finance attempts to explain price anomalies in terms of the biased behaviour of individuals, mostly concerned with the agents themselves and to a lesser degree aggregation of agent behaviour. Statistical finance is concerned with emergent properties arising from systems with many interacting agents and as such attempts to explain price anomalies in terms of the collective behaviour. Emergent properties are largely independent of the uniqueness of individual agents because they are dependent on the nature of the interactions of the agents rather than the agents themselves. This approach has drawn strongly on ideas arising from complex systems, phase transitions, criticality, self-organized criticality, non-extensivity (see Tsallis entropy), q-Gaussian models, and agents based models (see agent based model); as these are known to be able to recover some of phenomenology of financial market data, the stylized facts, in particular the long-range memory and scaling due to long-range interactions.

...
Wikipedia