On a Boltzmann-type price formation model
- 8 September 2013
- journal article
- Published by The Royal Society in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Vol. 469 (2157) , 20130126
Abstract
In this paper, we present a Boltzmann-type price formation model, which is motivated by a parabolic free boundary model for the evolution of price 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.Keywords
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This publication has 10 references indexed in Scilit:
- Price Dynamics in a Markovian Limit Order MarketSSRN Electronic Journal, 2012
- On a price formation free boundary model by Lasry and Lions: The Neumann problemComptes Rendus Mathematique, 2011
- On a price formation free boundary model by Lasry and LionsComptes Rendus Mathematique, 2011
- A Mathematical Approach to Order Book ModelingSSRN Electronic Journal, 2011
- A Stochastic Model for Order Book DynamicsOperations Research, 2010
- ON A PARABOLIC FREE BOUNDARY EQUATION MODELING PRICE FORMATIONMathematical Models and Methods in Applied Sciences, 2009
- Global Existence and Uniqueness of Solutions to a Model of Price FormationSIAM Journal on Mathematical Analysis, 2009
- Mean field gamesJapanese Journal of Mathematics, 2007
- Multi-agent-based Order Book Model of financial marketsEurophysics Letters, 2006
- Statistical properties of stock order books: empirical results and modelsQuantitative Finance, 2002