On a Boltzmann-type price formation model

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. © 2013 The Author(s) Published by the Royal Society. All rights reserved.

Citation
Burger, M., Caffarelli, L., Markowich, P. A., & Wolfram, M.-T. (2013). On a Boltzmann-type price formation model. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 469(2157), 20130126. doi:10.1098/rspa.2013.0126

Acknowledgements
L.C. was partially supported by a grant from the DMS division of the NSF. P. A. M. expresses his gratitude to the Humboldt Foundation for awarding the Humboldt ResearchAward to him, which allowed him to spend time with Martin Burger's research group in Munster, where this research was initiated. P. A. M. also acknowledges support from the Paris Foundation of Mathematics. M. T. W. acknowledges support from the Austrian Science Foundation FWF via the Hertha-Firnberg project no. T456-N23. We thank Bertram During (University of Sussex) for the useful hints to literature.

Publisher
The Royal Society

Journal
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

DOI
10.1098/rspa.2013.0126

arXiv
1302.5650

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