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arXiv · 1302.5650

On a Boltzmann type price formation model

Martin Burger·Luis Caffarelli·Peter Markowich·Marie-Therese Wolfram
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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.

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Martin Burger, Luis Caffarelli, Peter Markowich, Marie-Therese Wolfram. 2013-02-22. On a Boltzmann type price formation model. https://doi.org/10.1098/rspa.2013.0126

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