On a parabolic free boundary equation modeling price formation

Peter Markowich; N. Matevosyan; J. F. Pietschmann; Marie-Therese Wolfram

doi:10.1142/S0218202509003978

On a parabolic free boundary equation modeling price formation

Peter Markowich, N. Matevosyan, J. F. Pietschmann, Marie-Therese Wolfram

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

We discuss existence and uniqueness of solutions for a one-dimensional parabolic evolution equation with a free boundary. This problem was introduced by Lasry and Lions as description of the dynamical formation of the price of a trading good. Short time existence and uniqueness is established by a contraction argument. Then we discuss the issue of global-in-time-extension of the local solution which is closely related to the regularity of the free boundary. We also present numerical results.

Original language	English (US)
Pages (from-to)	1929-1957
Number of pages	29
Journal	Mathematical Models and Methods in Applied Sciences
Volume	19
Issue number	10
DOIs	https://doi.org/10.1142/S0218202509003978
State	Published - 2009
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: This publication is based on work supported by Award No. KUK-I1-007-43 of Peter Markowich, made by King Abdullah University of Science and Technology (KAUST) and by the Leverhulme Trust through the Research Grant entitled "KINETIC AND MEAN FIELD PARTIAL DIFFERENTIAL MODELS FOR SOCIO-ECONOMIC PROCESSES" (PI Peter Markowich).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

Keywords

Free boundary problem
Partial differential equations
Price formation

ASJC Scopus subject areas

Applied Mathematics
Modeling and Simulation

Access to Document

10.1142/S0218202509003978

Cite this

@article{57560db0657941a5bb59b43a9622262b,

title = "On a parabolic free boundary equation modeling price formation",

abstract = "We discuss existence and uniqueness of solutions for a one-dimensional parabolic evolution equation with a free boundary. This problem was introduced by Lasry and Lions as description of the dynamical formation of the price of a trading good. Short time existence and uniqueness is established by a contraction argument. Then we discuss the issue of global-in-time-extension of the local solution which is closely related to the regularity of the free boundary. We also present numerical results.",

keywords = "Free boundary problem, Partial differential equations, Price formation",

author = "Peter Markowich and N. Matevosyan and Pietschmann, {J. F.} and Marie-Therese Wolfram",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-I1-007-43 Acknowledgements: This publication is based on work supported by Award No. KUK-I1-007-43 of Peter Markowich, made by King Abdullah University of Science and Technology (KAUST) and by the Leverhulme Trust through the Research Grant entitled {"}KINETIC AND MEAN FIELD PARTIAL DIFFERENTIAL MODELS FOR SOCIO-ECONOMIC PROCESSES{"} (PI Peter Markowich). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2009",

doi = "10.1142/S0218202509003978",

language = "English (US)",

volume = "19",

pages = "1929--1957",

journal = "Mathematical Models and Methods in Applied Sciences",

issn = "0218-2025",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "10",

}

TY - JOUR

T1 - On a parabolic free boundary equation modeling price formation

AU - Markowich, Peter

AU - Matevosyan, N.

AU - Pietschmann, J. F.

AU - Wolfram, Marie-Therese

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-I1-007-43 Acknowledgements: This publication is based on work supported by Award No. KUK-I1-007-43 of Peter Markowich, made by King Abdullah University of Science and Technology (KAUST) and by the Leverhulme Trust through the Research Grant entitled "KINETIC AND MEAN FIELD PARTIAL DIFFERENTIAL MODELS FOR SOCIO-ECONOMIC PROCESSES" (PI Peter Markowich). This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2009

Y1 - 2009

N2 - We discuss existence and uniqueness of solutions for a one-dimensional parabolic evolution equation with a free boundary. This problem was introduced by Lasry and Lions as description of the dynamical formation of the price of a trading good. Short time existence and uniqueness is established by a contraction argument. Then we discuss the issue of global-in-time-extension of the local solution which is closely related to the regularity of the free boundary. We also present numerical results.

AB - We discuss existence and uniqueness of solutions for a one-dimensional parabolic evolution equation with a free boundary. This problem was introduced by Lasry and Lions as description of the dynamical formation of the price of a trading good. Short time existence and uniqueness is established by a contraction argument. Then we discuss the issue of global-in-time-extension of the local solution which is closely related to the regularity of the free boundary. We also present numerical results.

KW - Free boundary problem

KW - Partial differential equations

KW - Price formation

UR - http://www.scopus.com/inward/record.url?scp=72549117081&partnerID=8YFLogxK

U2 - 10.1142/S0218202509003978

DO - 10.1142/S0218202509003978

M3 - Article

AN - SCOPUS:72549117081

SN - 0218-2025

VL - 19

SP - 1929

EP - 1957

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

IS - 10

ER -

On a parabolic free boundary equation modeling price formation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this