The lattice Fokker–Planck equation for models of wealth distribution

Recent work on agent-based models of wealth distribution has yielded nonlinear, non-local Fokker–Planck equations whose steady-state solutions describe empirical wealth distributions with remarkable accuracy using only a few free parameters. Because these equations are often used to solve the ‘inverse problem’ of determining the free parameters given empirical wealth data, there is much impetus to find fast and accurate methods of solving the ‘forward problem’ of finding the steady state corresponding to given parameters. In this work, we derive and calibrate a lattice Boltzmann equation for this purpose. This article is part of the theme issue ‘Fluid dynamics, soft matter and complex systems: recent results and new methods’.