Journal of Applied Probability

Coupling limit order books and branching random walks

Florian Simatos

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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.

Article information

J. Appl. Probab., Volume 51, Number 3 (2014), 625-639.

First available in Project Euclid: 5 September 2014

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J85: Applications of branching processes [See also 92Dxx]
Secondary: 60G55: Point processes

Limit order book branching random walk branching random walk with a barrier


Simatos, Florian. Coupling limit order books and branching random walks. J. Appl. Probab. 51 (2014), no. 3, 625--639. doi:10.1239/jap/1409932663.

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