Limiting distribution for a simple model of order book dynamics

Łukasz Kruk

Open Mathematics (2012)

  • Volume: 10, Issue: 6, page 2283-2295
  • ISSN: 2391-5455

Abstract

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A continuous-time model for the limit order book dynamics is considered. The set of outstanding limit orders is modeled as a pair of random counting measures and the limiting distribution of this pair of measure-valued processes is obtained under suitable conditions on the model parameters. The limiting behavior of the bid-ask spread and the midpoint of the bid-ask interval are also characterized.

How to cite

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Łukasz Kruk. "Limiting distribution for a simple model of order book dynamics." Open Mathematics 10.6 (2012): 2283-2295. <http://eudml.org/doc/269746>.

@article{ŁukaszKruk2012,
abstract = {A continuous-time model for the limit order book dynamics is considered. The set of outstanding limit orders is modeled as a pair of random counting measures and the limiting distribution of this pair of measure-valued processes is obtained under suitable conditions on the model parameters. The limiting behavior of the bid-ask spread and the midpoint of the bid-ask interval are also characterized.},
author = {Łukasz Kruk},
journal = {Open Mathematics},
keywords = {Order book dynamics; Bid-ask spread; Utility; Waiting costs; Measure-valued process; Weak convergence; Laplace transform; order book dynamics; bid-ask spread; utility; waiting costs; measure-valued process; weak convergence},
language = {eng},
number = {6},
pages = {2283-2295},
title = {Limiting distribution for a simple model of order book dynamics},
url = {http://eudml.org/doc/269746},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Łukasz Kruk
TI - Limiting distribution for a simple model of order book dynamics
JO - Open Mathematics
PY - 2012
VL - 10
IS - 6
SP - 2283
EP - 2295
AB - A continuous-time model for the limit order book dynamics is considered. The set of outstanding limit orders is modeled as a pair of random counting measures and the limiting distribution of this pair of measure-valued processes is obtained under suitable conditions on the model parameters. The limiting behavior of the bid-ask spread and the midpoint of the bid-ask interval are also characterized.
LA - eng
KW - Order book dynamics; Bid-ask spread; Utility; Waiting costs; Measure-valued process; Weak convergence; Laplace transform; order book dynamics; bid-ask spread; utility; waiting costs; measure-valued process; weak convergence
UR - http://eudml.org/doc/269746
ER -

References

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  7. [7] Karatzas I., Shreve S.E., Brownian Motion and Stochastic Calculus, Grad. Texts in Math., 113, Springer, New York, 1988 Zbl0638.60065
  8. [8] Kruk Ł., Functional limit theorems for a simple auction, Math. Oper. Res., 2003, 28(4), 716–751 http://dx.doi.org/10.1287/moor.28.4.716.20519[Crossref] Zbl1082.91044
  9. [9] Luckock H., A steady-state model of the continuous double auction, Quant. Finance, 2003, 3(5), 385–404 http://dx.doi.org/10.1088/1469-7688/3/5/305[Crossref] 
  10. [10] Mendelson H., Market behavior in a clearing house, Econometrica, 1982, 50(6), 1505–1524 http://dx.doi.org/10.2307/1913393[Crossref] Zbl0502.90009
  11. [11] Roşu I., A dynamic model of the limit order book, Review of Financial Studies, 2009, 22(11), 4601–4641 http://dx.doi.org/10.1093/rfs/hhp011[Crossref] 

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