On a price formation free boundary model by Lasry & Lions: The Neumann problem
Luis A. Caffarelli, Peter A. Markowich, Marie-Therese Wolfram
TL;DR
This paper analyzes a free boundary model for price formation using a transformation to the heat equation, establishing existence, uniqueness, and behavior of solutions with Neumann boundary conditions.
Contribution
It introduces a transformation approach to solve the model explicitly and discusses conditions for global existence and non-existence of solutions.
Findings
Explicit solutions for the free boundary problem
Conditions for global existence of solutions
Examples of non-existence cases
Abstract
We discuss local and global existence and uniqueness for the price formation free boundary model with homogeneous Neumann boundary conditions introduced by Lasry & Lions in 2007. The results are based on a transformation of the problem to the heat equation with nonstandard boundary conditions. The free boundary becomes the zero level set of the solution of the heat equation. The transformation allows us to construct an explicit solution and discuss the behavior of the free boundary. Global existence can be verified under certain conditions on the free boundary and examples of non-existence are given.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals · Theoretical and Computational Physics · Economic theories and models