ON A PARABOLIC FREE BOUNDARY EQUATION MODELING PRICE FORMATION

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

Research output: Contribution to journalArticlepeer-review

20 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 languageEnglish (US)
Pages (from-to)1929-1957
Number of pages29
JournalMathematical Models and Methods in Applied Sciences
Volume19
Issue number10
DOIs
StatePublished - Nov 21 2011
Externally publishedYes

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