In this paper we propose an extension of the Lasry-Lions price formation model which includes uctuations of the numbers of buyers and vendors. We analyze the model in the case of deterministic and stochastic market size uctuations and present results on the long time asymptotic behavior and numerical evidence and conjectures on periodic, almost periodic, and stochastic uctuations. The numerical simulations extend the theoretical statements and give further insights into price formation dynamics.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The first author was partially supported by the NSF. The last author was financially supported by the Austrian Academy of Sciences ( ÖAW) via the New Frontiers Group, NFG-001.