Kinetic models for optimal control of wealth inequalities

D¨uring, Bertram, Pareschi, Lorenzo and Toscani, Giuseppe (2018) Kinetic models for optimal control of wealth inequalities. European Physical Journal B: Condensed Matter and Complex Systems. ISSN 1434-6028

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Abstract

We introduce and discuss optimal control strategies for kinetic models for wealth distribution in a simple market economy, acting to minimize the variance of the wealth density among the population. Our analysis is based on a finite time horizon approximation, or model predictive control, of the corresponding control problem for the microscopic agents' dynamic and results in an alternative theoretical approach to the taxation and redistribution policy at a global level. It is shown that in general the control is able to modify the Pareto index of the stationary solution of the corresponding Boltzmann kinetic equation, and that this modification can be exactly quantified. Connections between previous Fokker-Planck based models and taxation-redistribution policies and the present approach are also discussed.

Item Type: Article
Keywords: Wealth distribution, wealth inequalities, kinetic models, optimal control, finite time horizon, Fokker-Planck equations, Pareto tails, taxation, redistribution.
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Numerical Analysis and Scientific Computing Research Group
Subjects: Q Science > QA Mathematics
Depositing User: Jodie Bacon
Date Deposited: 13 Aug 2018 09:44
Last Modified: 29 Oct 2018 15:45
URI: http://sro.sussex.ac.uk/id/eprint/77755

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