Fluctuation analysis of the three agent groups herding model

TL;DR

This paper develops a stochastic differential equation model for three-agent herding dynamics, capturing complex socio-economic behaviors and reproducing empirical financial market return statistics.

Contribution

It introduces a novel three-agent herding model with extensions for exogenous noise, enhancing the understanding of market dynamics and agent interactions.

Findings

Reproduces power law statistics of financial returns

Models complex agent interactions with herding behavior

Extensible framework for socio-economic systems

Abstract

We derive a system of stochastic differential equations simulating the dynamics of the three agent groups with herding interaction. Proposed approach can be valuable in the modeling of the complex socio-economic systems with similar composition of the agents. We demonstrate how the sophisticated statistical features of the absolute return in the financial markets can be reproduced by extending the herding interaction of the agents and introducing the third agent state. As well we consider possible extension of proposed herding model introducing additional exogenous noise. Such consistent microscopic and macroscopic model precisely reproduces empirical power law statistics of the return in the financial markets.