# A kinetic description for the herding behavior in financial market

## TL;DR

This paper develops a kinetic framework for herding behavior in financial markets, establishing measure-valued solutions and analyzing herding phenomena with different energy functionals, including conditions for exponential herding rates.

## Contribution

It derives a kinetic herding model from a particle system, proves existence of solutions, and analyzes herding behavior with new energy functionals under various conditions.

## Key findings

- Existence of measure-valued solutions for the kinetic herding model.
- Herding behavior can be characterized without restrictions on parameters.
- Exponential herding rate established under certain conditions.

## Abstract

As a continuation of the study of the herding model proposed in (Bae et al. in arXiv:1712.01085, 2017), we consider in this paper the derivation of the kinetic version of the herding model, the existence of the measure-valued solution and the corresponding herding behavior at the kinetic level. We first consider the mean-field limit of the particle herding model and derive the existence of the measure-valued solutions for the kinetic herding model. We then study the herding phenomena of the solutions in two different ways by introducing two different types of herding energy functionals. First, we derive a herding phenomena of the measure-valued solutions under virtually no restrictions on the parameter sets using the Barbalat's lemma. We, however, don't get any herding rate in this case. On the other hand, we also establish a Gr\"onwall type estimate for another herding functional, leading to the exponential herding rate, under comparatively strict conditions. These results are then extended to smooth solutions.