From Disequilibrium Markets to Equilibrium

TL;DR

This paper investigates how disequilibrium models in financial markets transition to equilibrium, using mathematical reduction techniques and stability analysis, supported by numerical examples to illustrate the process and implications.

Contribution

It introduces a mathematical framework for analyzing the passage from disequilibrium to equilibrium in financial models, specifically applying Tikhonov-Fenichel reduction to the Beja-Goldman model.

Findings

The disequilibrium-to-equilibrium transition can be rigorously characterized mathematically.

Stability properties of the reduced equilibrium model are analyzed.

Numerical examples support the theoretical analysis and illustrate the transition process.

Abstract

The modeling of financial markets as disequilibrium models by ordinary differential equations has become a popular modeling tool. One famous example of such a model is the Beja-Goldman model(The Journal of Finance, 1980) which we consider in this paper. We study the passage from disequilibrium dynamics to equilibrium. Mathematically, this limit corresponds to an asymptotic limit also known as a Tikhonov-Fenichel reduction. Furthermore, we analyze the stability of the reduced equilibrium model and discuss the economic implications. We conduct several numerical examples to visualize and support our analysis.