Communications in Mathematical Sciences

Volume 12 (2014)

Number 7

On the asymptotic behavior of a Boltzmann-type price formation model

Pages: 1353 – 1361

(Fast Communication)

DOI: http://dx.doi.org/10.4310/CMS.2014.v12.n7.a10

Authors

Martin Burger (Institute for Computational and Applied Mathematics, Münster, Germany)

Luis Caffarelli (Department of Mathematics, University of Texas at Austin, Tx. U.S.A.)

Peter A. Markowich (Department of Applied Mathematics and Theoretical Physics, University of Cambridge, United Kingdom)

Marie-Therese Wolfram (King Abdullah University of Science and Technology, Thuwal, Saudi Arabia)

Abstract

In this paper we study the asymptotic behavior of a Boltzmann-type price formation model, which describes the trading dynamics in a financial market. In many of these markets trading happens at high frequencies and low transaction costs. This observation motivates the study of the limit as the number of transactions $k$ tends to infinity, the transaction cost $a$ to zero and $ka = \textit{const}$. Furthermore we illustrate the price dynamics with numerical simulations.

Keywords

Boltzmann-type equation, price formation, asymptotic behavior

2010 Mathematics Subject Classification

35B40, 35K20, 91B60

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