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Coupling Limit Order Books and Branching Random Walks

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  30 January 2018

Florian Simatos
Florian Simatos*
Affiliation:
Eindhoven University of Technology
*
∗ Postal address: Mathematics and Computer Science Department, Eindhoven University of Technology, MF 4.097a, PO Box 513, 5600 MB Eindhoven, The Netherlands. Email address: f.simatos@tue.nl
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Abstract

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We consider a model for a one-sided limit order book proposed by Lakner, Reed and Stoikov (2013). We show that it can be coupled with a branching random walk and use this coupling to answer a nontrivial question about the long-term behavior of the price. The coupling relies on a classical idea of enriching the state space by artificially creating a filiation, in this context between orders of the book, which we believe has the potential of being useful for a broader class of models.

Keywords

Limit order bookbranching random walkbranching random walk with a barrier

MSC classification

Primary: 60J85: Applications of branching processes
Secondary: 60G55: Point processes
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 3 , September 2014 , pp. 625 - 639
Copyright
© Applied Probability Trust 

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