  In this paper we propose an extension of the Lasry-Lions price formation
model which includes fluctuations of the numbers of buyers and vendors. We
analyze the model in the case of deterministic and stochastic market size
fluctuations and present results on the long time asymptotic behavior and
numerical evidence and conjectures on periodic, almost periodic and stochastic
fluctuations. The numerical simulations extend the theoretical statements and
give further insights into price formation dynamics.
