ON A PARABOLIC FREE BOUNDARY EQUATION MODELING PRICE FORMATION

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

ON A PARABOLIC FREE BOUNDARY EQUATION MODELING PRICE FORMATION

Type

Article

Authors

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

KAUST Grant Number

KUK-I1-007-43

Online Publication Date

2011-11-21

Print Publication Date

2009-10

Date

2011-11-21

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.

Citation

MARKOWICH PA, MATEVOSYAN N, PIETSCHMANN J-F, WOLFRAM M-T (2009) ON A PARABOLIC FREE BOUNDARY EQUATION MODELING PRICE FORMATION. Mathematical Models and Methods in Applied Sciences 19: 1929–1957. Available: http://dx.doi.org/10.1142/S0218202509003978.

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).