On a Boltzmann type price formation model

TL;DR

This paper introduces a Boltzmann type price formation model inspired by a free boundary model, analyzes its mathematical properties, and demonstrates convergence to the classical model with numerical simulations.

Contribution

It presents a novel Boltzmann type model for price formation and proves its solutions converge to the established Lasry-Lions model as transaction rates increase.

Findings

Solutions converge to Lasry-Lions model as transaction rate increases

Initial layer behavior analyzed on fast time scale

Numerical experiments illustrate price dynamics

Abstract

In this paper we present a Boltzmann type price formation model, which is motivated by a parabolic free boundary model for the evolution of the prize presented by Lasry and Lions in 2007. We discuss the mathematical analysis of the Boltzmann type model and show that its solutions converge to solutions of the model by Lasry and Lions as the transaction rate tends to infinity. Furthermore we analyse the behaviour of the initial layer on the fast time scale and illustrate the price dynamics with various numerical experiments.