Kinetic models for optimal control of wealth inequalities

Bertram Düring, Lorenzo Pareschi, Giuseppe Toscani (6/3/2018, preprint arXiv:1803.02171)

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 model predictive control approximation of the microscopic agents' dynamic and results in an alternative theoretical approach to the taxation and redistribution policy.

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.