On a Boltzmann-type price formation model

Handle URI:
http://hdl.handle.net/10754/562824
Title:
On a Boltzmann-type price formation model
Authors:
Burger, Martin; Caffarelli, Luis A.; Markowich, Peter A. ( 0000-0002-3704-1821 ) ; Wolfram, Marie Therese
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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Publisher:
The Royal Society
Journal:
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue Date:
26-Jun-2013
DOI:
10.1098/rspa.2013.0126
Type:
Article
ISSN:
13645021
Sponsors:
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.
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorBurger, Martinen
dc.contributor.authorCaffarelli, Luis A.en
dc.contributor.authorMarkowich, Peter A.en
dc.contributor.authorWolfram, Marie Thereseen
dc.date.accessioned2015-08-03T11:11:40Zen
dc.date.available2015-08-03T11:11:40Zen
dc.date.issued2013-06-26en
dc.identifier.issn13645021en
dc.identifier.doi10.1098/rspa.2013.0126en
dc.identifier.urihttp://hdl.handle.net/10754/562824en
dc.description.abstractIn 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.en
dc.description.sponsorshipL.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.en
dc.publisherThe Royal Societyen
dc.subjectAsymptoticsen
dc.subjectBoltzmann-type equationen
dc.subjectFree boundaryen
dc.subjectNumerical simulationsen
dc.subjectPrice formationen
dc.titleOn a Boltzmann-type price formation modelen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciencesen
dc.contributor.institutionInstitute for Computational and Applied Mathematics, University of Münster, Einsteinstrasse 62, 48149 Münstere, Germanyen
dc.contributor.institutionUniversity of Texas at Austin, 1 University Station, C120, Austin TX 78712-1082, United Statesen
dc.contributor.institutionDepartment of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Vienna, Austriaen
kaust.authorMarkowich, Peter A.en
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