  In this paper we present a Boltzmann type price formation model, which is
motivated by a parabolic free boundary model for the evolution of the prize
presented by Lasry and Lions in 2007. We discuss the mathematical analysis of
the Boltzmann type model and show that its solutions converge to solutions of
the model by Lasry and Lions as the transaction rate tends to infinity.
Furthermore we analyse the behaviour of the initial layer on the fast time
scale and illustrate the price dynamics with various numerical experiments.
