  The recent book by T. Piketty (Capital in the Twenty-First Century) promoted
the important issue of wealth inequality. In the last twenty years, physicists
and mathematicians developed models to derive the wealth distribution using
discrete and continuous stochastic processes (random exchange models) as well
as related Boltzmann-type kinetic equations. In this literature, the usual
concept of equilibrium in Economics is either replaced or completed by
statistical equilibrium.
  In order to illustrate this activity with a concrete example, we present a
stylised random exchange model for the distribution of wealth. We first discuss
a fully discrete version (a Markov chain with finite state space). We then
study its discrete-time continuous-state-space version and we prove the
existence of the equilibrium distribution. Finally, we discuss the connection
of these models with Boltzmann-like kinetic equations for the marginal
distribution of wealth. This paper shows in practice how it is possible to
start from a finitary description and connect it to continuous models following
Boltzmann's original research program.

Probability;Physics and Society;General Finance