Kinetic models for optimal control of wealth inequalities

  • Bertram DüringEmail author
  • Lorenzo Pareschi
  • Giuseppe Toscani
Open Access
Regular Article


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 for taxation-redistribution policies and the present approach are also discussed.


Statistical and Nonlinear Physics 


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© The Author(s) 2018

Open AccessThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Sussex, Pevensey IIBrightonUK
  2. 2.Dipartimento di Matematica e InformaticaFerraraItaly
  3. 3.Dipartimento di Matematica and IMATI, CNRPaviaItaly

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