ON A PARABOLIC FREE BOUNDARY EQUATION MODELING PRICE FORMATION

P. A. Markowich; N. Matevosyan; J. -F. Pietschmann; M. -T. Wolfram

doi:10.1142/S0218202509003978

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ON A PARABOLIC FREE BOUNDARY EQUATION MODELING PRICE FORMATION

Journal article

Peer reviewed

ON A PARABOLIC FREE BOUNDARY EQUATION MODELING PRICE FORMATION

P. A. Markowich, N. Matevosyan, J. -F. Pietschmann and M. -T. Wolfram

Mathematical models & methods in applied sciences, Vol.19(10), pp.1929-1957

10/2009

DOI: https://doi.org/10.1142/S0218202509003978

Abstract

Mathematics

Mathematics, Applied

Physical Sciences

Science & Technology

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.

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Title: ON A PARABOLIC FREE BOUNDARY EQUATION MODELING PRICE FORMATION
Creators - without role: P. A. Markowich - University of Cambridge
N. Matevosyan - University of Cambridge
J. -F. Pietschmann - University of Cambridge
M. -T. Wolfram - University of Cambridge
Publication Details: Mathematical models & methods in applied sciences, Vol.19(10), pp.1929-1957
Publisher: World Scientific
Number of pages: 29
Grant note: KUK-I1-007-43 / King Abdullah University of Science and Technology (KAUST); King Abdullah University of Science & Technology Leverhulme Trust
Identifiers: 9944618808331
Academic Unit: King Abdullah University of Science & Technology
Language: English
Resource Type: Journal article