Wealth distribution in presence of debts: A Fokker–Planck description

Torregrossa, Marco; Toscani, Giuseppe

doi:10.4310/cms.2018.v16.n2.a11

Cited by 20 publications

(18 citation statements)

References 35 publications

(84 reference statements)

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“…In the linear case, the resulting Fokker-Planck description possesses a steady state distribution of shape identical to that resulting from the Maxwellian one. However its solution, in contrast with the Maxwellian description [68,69], has been shown to converge exponentially fast in relative Shannon entropy towards equilibrium with an explicit rate for a class of regular initial data, and to converge exponentially in L 1 (R + ) at explicit rate for all initial densities that have bounded relative entropy with respect to the equilibrium density.…”

Section: Discussionmentioning

confidence: 95%

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Non-Maxwellian kinetic equations modeling the dynamics of wealth distribution

Toscani

Pulvirenti

Terraneo

2020

Math. Models Methods Appl. Sci.

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We introduce a class of new one-dimensional linear Fokker-Planck type equations describing the evolution in time of the 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.

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Section: Discussionmentioning

confidence: 95%

“…also Ref. [69]), this type of inequalities do not seem to be available in presence of variable diffusion coefficients as they are those in (1.1).…”

Section: Introductionmentioning

confidence: 99%

Non-Maxwellian kinetic equations modeling the dynamics of wealth distribution

Toscani

Pulvirenti

Terraneo

2020

Math. Models Methods Appl. Sci.

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“…The study of convergence rates for this new class of Fokker-Planck equations has been developed in recent years, by adapting the study of the decay in relative entropy to the new situation of variable coefficient of diffusion [20,41,42]. These studies were complemented with the consideration of new differential inequalities, like Chernoff inequality [13,19,28], that appeared essential to prove convergence towards equilibria with fat tails.…”

Section: Introductionmentioning

confidence: 99%

On a class of Fokker-Planck equations with subcritical confinement

Toscani¹,

Zanella²

2021

Preprint

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We study the relaxation to equilibrium for a class linear onedimensional Fokker-Planck equations characterized by a particular subcritical confinement potential. An interesting feature of this class of Fokker-Planck equations is that, for any given probability density e(x), the diffusion coefficient can be built to have e(x) as steady state. This representation of the equilibrium density can be fruitfully used to obtain one-dimensional Wirtinger-type inequalities and to recover, for a sufficiently regular density e(x), a polynomial rate of convergence to equilibrium. Numerical results then confirm the theoretical analysis, and allow to conjecture that convergence to equilibrium with positive rate still holds for steady states characterized by a very slow polynomial decay at infinity.

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“…These results refer to the case δ = 0. Several studies then made use of this equation, still with δ = 0, to describe various problems related to the time-evolution of wealth density towards a Pareto-type equilibrium in a trading society [3,[37][38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Economic Segregation Under the Action of Trading Uncertainties

et al. 2020

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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.

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Wealth distribution in presence of debts: A Fokker–Planck description

Cited by 20 publications

References 35 publications

Non-Maxwellian kinetic equations modeling the dynamics of wealth distribution

Non-Maxwellian kinetic equations modeling the dynamics of wealth distribution

On a class of Fokker-Planck equations with subcritical confinement

Economic Segregation Under the Action of Trading Uncertainties

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