Parabolic free boundary price formation models under market size fluctuations

TL;DR

This paper extends the Lasry-Lions price formation model to include market size fluctuations, analyzing both deterministic and stochastic cases, and providing numerical simulations to understand long-term behavior and price dynamics.

Contribution

It introduces a novel extension of the Lasry-Lions model incorporating market size fluctuations and analyzes their impact on price formation.

Findings

Long-term asymptotic behavior characterized

Numerical simulations support theoretical results

Conjectures on periodic and stochastic fluctuations

Abstract

In this paper we propose an extension of the Lasry-Lions price formation model which includes fluctuations of the numbers of buyers and vendors. We analyze the model in the case of deterministic and stochastic market size fluctuations and present results on the long time asymptotic behavior and numerical evidence and conjectures on periodic, almost periodic and stochastic fluctuations. The numerical simulations extend the theoretical statements and give further insights into price formation dynamics.