On a price formation free boundary model by Lasry & Lions

TL;DR

This paper analyzes a free boundary model for price formation introduced by Lasry & Lions, establishing global existence, regularity, and asymptotic behavior by transforming the problem into the heat equation.

Contribution

It introduces a novel approach transforming the free boundary problem into the heat equation to analyze its properties.

Findings

Proves global existence of solutions.

Establishes regularity of the free boundary.

Describes asymptotic behavior of the model.

Abstract

We discuss global existence and asymptotic behaviour of a price formation free boundary model introduced by Lasry & Lions in 2007. Our results are based on a construction which transforms the problem into the heat equation with specially prepared initial datum. The key point is that the free boundary present in the original problem becomes the zero level set of this solution. Using the properties of the heat operator we can show global existence, regularity and asymptotic results of the free boundary.