ON A PARABOLIC FREE BOUNDARY EQUATION MODELING PRICE FORMATION

P. A. MARKOWICH; N. MATEVOSYAN; J.-F. PIETSCHMANN; M.-T. WOLFRAM

doi:10.1142/S0218202509003978

ON A PARABOLIC FREE BOUNDARY EQUATION MODELING PRICE FORMATION

P. A. MARKOWICH, N. MATEVOSYAN, J.-F. PIETSCHMANN, M.-T. WOLFRAM

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

21 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. © 2009 World Scientific Publishing Company.

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 - Nov 21 2011
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.

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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. {\textcopyright} 2009 World Scientific Publishing Company.",

author = "MARKOWICH, {P. A.} and N. MATEVOSYAN and J.-F. PIETSCHMANN and M.-T. 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 = "2011",

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doi = "10.1142/S0218202509003978",

language = "English (US)",

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AU - MATEVOSYAN, N.

AU - PIETSCHMANN, J.-F.

AU - WOLFRAM, M.-T.

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 - 2011/11/21

Y1 - 2011/11/21

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. © 2009 World Scientific Publishing Company.

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. © 2009 World Scientific Publishing Company.

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SN - 0218-2025

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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

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