Global existence and uniqueness of solutions to a model of price formation

TL;DR

This paper proves that solutions to a specific 1-D price formation model with free boundary and dynamic sources exist uniquely for all time, ensuring the model's mathematical robustness.

Contribution

It establishes global existence and uniqueness for a price formation model involving a free boundary and non-standard sources, advancing the mathematical understanding of such models.

Findings

Proved global existence of solutions.

Established uniqueness of solutions.

Validated the model's mathematical consistency.

Abstract

We study a model due to J.M. Lasry and P.L. Lions, describing the evolution of a scalar price which is realized as a free boundary in a 1-D diffusion equation with dynamically evolving, non-standard sources. We establish global existence and uniqueness.