Mesoscopic modelling of financial markets

Abstract

We derive a mesoscopic description of the behavior of a simple financial market where the agents can create their own portfolio between two investment alternatives: a stock and a bond. The model is derived starting from the Levy-Levy-Solomon microscopic model (Econ. Lett., 45, (1994), 103--111) using the methods of kinetic theory and consists of a linear Boltzmann equation for the wealth distribution of the agents coupled with an equation for the price of the stock. From this model, under a suitable scaling, we derive a Fokker-Planck equation and show that the equation admits a self-similar lognormal behavior. Several numerical examples are also reported to validate our analysis.

References in corpus (1)

• Self-similarity and power-like tails in nonconservative kinetic models

Cited by in corpus (12)

• Wealth distribution under the spread of infectious diseases
• Wealth distribution and collective knowledge. A Boltzmann approach
• Kinetic models for the trading of goods
• Explicit equilibria in a kinetic model of gambling
• Kinetic modeling of alcohol consumption
• The size distribution of cities: a kinetic explanation
• Effect of tax dynamics on linearly growing processes under stochastic resetting: a possible economic model
• Kinetic models for goods exchange in a multi-agent market
• A revisited Johnson-Mehl-Avrami-Kolmogorov model and the evolution of grain-size distributions in steel
• Boltzmann and Fokker-Planck equations modelling the Elo rating system with learning effects
• An Elo-type rating model for players and teams of variable strength
• Mean Field Limit of a Behavioral Financial Market Model