On a Boltzmann-type price formation model-Reference-Cited by-同舟云学术

On a Boltzmann-type price formation model

Published:2013-09-08 Issue:2157 Volume:469 Page:20130126
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Burger Martin¹,Caffarelli Luis²,Markowich Peter A.³,Wolfram Marie-Therese⁴

Affiliation:

1. Institute for Computational and Applied Mathematics, University of Münster, Einsteinstrasse 62, 48149 Münster, Germany

2. University of Texas at Austin, 1 University Station, C120, Austin, TX 78712-1082, USA

3. Computer, Electrical and Mathematical Sciences and Engineering Division, 4700 King Abdullah University of Science and Technology, Thuwal 23955-6900, Kingdom of Saudi Arabia

4. Department of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Vienna, Austria

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 price 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.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2013.0126

Reference13 articles.

1. Mean field games

2. ON A PARABOLIC FREE BOUNDARY EQUATION MODELING PRICE FORMATION

3. Global Existence and Uniqueness of Solutions to a Model of Price Formation

4. On a price formation free boundary model by Lasry and Lions

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