Power Laws and Symmetries in a Minimal Model of Financial Market Economy

TL;DR

This paper introduces a minimal analytical model of financial markets based on symmetry constraints, revealing universal power-law behaviors and linking model parameters to real market measurements.

Contribution

It presents a novel minimal microscopic model of financial markets that analytically captures power-law behaviors and relates parameters to observable market quantities.

Findings

Universal power-law-like behaviors depend on each other, similar to critical exponents.

Model parameters can be related to measurable real market quantities.

Analytical solutions provide insights into social and economic phenomena.

Abstract

A financial market is a system resulting from the complex interaction between participants in a closed economy. We propose a minimal microscopic model of the financial market economy based on the real economy's symmetry constraint and minimality requirement. We solve the proposed model analytically in the mean-field regime, which shows that various kinds of universal power-law-like behaviors in the financial market may depend on one another, just like the critical exponents in physics. We then discuss the parameters in the proposed model, and we show that each parameter in our model can be related to measurable quantities in the real market, which enables us to discuss the cause of a few kinds of social and economic phenomena.