scholarly journals Fokker–Planck description of wealth dynamics and the origin of Pareto's law

2014 ◽  
Vol 25 (12) ◽  
pp. 1441008 ◽  
Author(s):  
Bruce Boghosian
Keyword(s):  
Recent Work ◽  
Wealth Distribution ◽  
Planck Equation ◽  
Economic Agents ◽  
Distribution Of Wealth ◽  
Fokker Planck Equation ◽  
Wealth Redistribution ◽  
Pareto’S Law ◽  
Fokker Planck

The so-called "Yard-Sale Model" of wealth distribution posits that wealth is transferred between economic agents as a result of transactions whose size is proportional to the wealth of the less wealthy agent. In recent work [B. M. Boghosian, Phys. Rev. E89, 042804 (2014)], it was shown that this results in a Fokker–Planck equation governing the distribution of wealth. With the addition of a mechanism for wealth redistribution, it was further shown that this model results in stationary wealth distributions that are very similar in form to Pareto's well-known law. In this paper, a much simpler derivation of that Fokker–Planck equation is presented.

Non-Maxwellian kinetic equations modeling the dynamics of wealth distribution

2020 ◽  
Vol 30 (04) ◽  
pp. 685-725 ◽  
Author(s):  
Giulia Furioli ◽  
Ada Pulvirenti ◽  
Elide Terraneo ◽  
Giuseppe Toscani
Keyword(s):  
Steady State ◽  
Wealth Distribution ◽  
Kinetic Equations ◽  
Planck Equation ◽  
Logarithmic Sobolev Inequality ◽  
One Dimensional ◽  
Distribution Of Wealth ◽  
Multi Agent ◽  
Fokker Planck Equations ◽  
Fokker Planck

We introduce a class of new one-dimensional linear Fokker–Planck-type equations describing the dynamics of the distribution of wealth in a multi-agent society. The equations are obtained, via a standard limiting procedure, by introducing an economically relevant variant to the kinetic model introduced in 2005 by Cordier, Pareschi and Toscani according to previous studies by Bouchaud and Mézard. The steady state of wealth predicted by these new Fokker–Planck equations remains unchanged with respect to the steady state of the original Fokker–Planck equation. However, unlike the original equation, it is proven by a new logarithmic Sobolev inequality with weight and classical entropy methods that the solution converges exponentially fast to equilibrium.

scholarly journals Economic Segregation Under the Action of Trading Uncertainties

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1390
Author(s):  
Elena Ballante ◽  
Chiara Bardelli ◽  
Mattia Zanella ◽  
Silvia Figini ◽  
Giuseppe Toscani
Keyword(s):  
Statistical Study ◽  
Wealth Distribution ◽  
Planck Equation ◽  
Type Equation ◽  
Statistical Information ◽  
Uncertain Parameters ◽  
Social Forces ◽  
Economic Segregation ◽  
Distribution Of Wealth ◽  
Fokker Planck

We study the distribution of wealth in a market economy in which the trading propensity of the agents is uncertain. Our approach is based on kinetic models for collective phenomena, which, at variance with the classical kinetic theory of rarefied gases, has to face the lack of fundamental principles, which are replaced by empirical social forces of which we have at most statistical information. The proposed kinetic description allows recovering emergent wealth distribution profiles, which are described by the steady states of a Fokker–Planck-type equation with uncertain parameters. A statistical study of the stationary profiles of the Fokker–Planck equation then shows that the wealth distribution can develop a multimodal shape in the presence of observable highly stressful economic situations.

scholarly journals On a Fokker-Planck equation for wealth distribution

2018 ◽  
Vol 11 (2) ◽  
pp. 337-355 ◽  
Author(s):  
Marco Torregrossa ◽  
◽  
Giuseppe Toscani ◽  
Keyword(s):  
Wealth Distribution ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

AN APPLICATION OF FOKKER–PLANCK EQUATION TO JOSEPHSON JUNCTION

1989 ◽  
Vol 9 (1) ◽  
pp. 109-120
Author(s):  
G. Liao ◽  
A.F. Lawrence ◽  
A.T. Abawi
Keyword(s):  
Josephson Junction ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

scholarly journals Time-changed fractional Ornstein-Uhlenbeck process

2020 ◽  
Vol 23 (2) ◽  
pp. 450-483 ◽  
Author(s):  
Giacomo Ascione ◽  
Yuliya Mishura ◽  
Enrica Pirozzi
Keyword(s):  
Planck Equation ◽  
Uhlenbeck Process ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Fokker Planck

AbstractWe define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

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