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2012 | 10 | 6 | 2283-2295
Tytuł artykułu

Limiting distribution for a simple model of order book dynamics

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Języki publikacji
EN
Abstrakty
EN
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.
Twórcy
autor
  • Department of Mathematics, Maria Curie-Skłodowska University, Pl. Marii Curie-Skłodowskiej 1, 20-031, Lublin, Poland, lkruk@hektor.umcs.lublin.pl
Bibliografia
  • [1] Asmussen S., Applied Probability and Queues, 2nd ed., Appl. Math. (N.Y.), 51, Springer, New York, 2003
  • [2] Bayraktar E., Horst U., Sircar R., Queueing theoretic approaches to financial price fluctuations, In: Financial Engineering, Handbooks Oper. Res. Management Sci., 15, Elsevier/North-Holland, Amsterdam, 2007, 637–677
  • [3] Cont R., Stoikov S., Talreja R., A stochastic model for order book dynamics, Oper. Res., 2010, 58(3), 549–563 http://dx.doi.org/10.1287/opre.1090.0780[Crossref][WoS]
  • [4] Doytchinov B., Lehoczky J., Shreve S., Real-time queues in heavy traffic with earliest-deadline-first queue discipline, Ann. Appl. Probab., 2001, 11(2), 332–378 http://dx.doi.org/10.1214/aoap/1015345295[Crossref]
  • [5] Ethier S.N., Kurtz T.G., Markov Processes. Characterization and Convergence, Wiley Ser. Probab. Math. Statist., John Wiley & Sons, New York, 1986
  • [6] Iglehart D.L., Whitt W., Multiple channel queues in heavy traffic. I, Adv. in Appl. Probab., 1970, 2(1), 150–177 http://dx.doi.org/10.2307/3518347[Crossref]
  • [7] Karatzas I., Shreve S.E., Brownian Motion and Stochastic Calculus, Grad. Texts in Math., 113, Springer, New York, 1988
  • [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]
  • [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] Mendelson H., Market behavior in a clearing house, Econometrica, 1982, 50(6), 1505–1524 http://dx.doi.org/10.2307/1913393[Crossref]
  • [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]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0098-3
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