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Rigorous results for the Stigler-Luckock model for the evolution of an order book
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SYSNO ASEP 0490719 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Rigorous results for the Stigler-Luckock model for the evolution of an order book Tvůrce(i) Swart, Jan M. (UTIA-B) RID, ORCID Celkový počet autorů 1 Zdroj.dok. Annals of Applied Probability. - : Institute of Mathematical Statistics - ISSN 1050-5164
Roč. 28, č. 3 (2018), s. 1491-1535Poč.str. 45 s. Forma vydání Tištěná - P Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova Continuous double auction ; order book ; rank-based Markov chain ; self-organized criticality ; Stigler-Luckock model ; market microstructure Vědní obor RIV BA - Obecná matematika Obor OECD Pure mathematics CEP GA16-15238S GA ČR - Grantová agentura ČR GAP201/12/2613 GA ČR - Grantová agentura ČR Institucionální podpora UTIA-B - RVO:67985556 UT WOS 000434140900006 EID SCOPUS 85048045652 DOI 10.1214/17-AAP1336 Anotace In 1964, G. J. Stigler introduced a stochastic model for the evolution of an order book on a stock market. This model was independently rediscovered and generalized by H. Luckock in 2003. In his formulation, traders place buy and sell limit orders of unit size according to independent Poisson processes with possibly different intensities. Newly arriving buy (sell) orders are either immediately matched to the best available matching sell (buy) order or stay in the order book until a matching order arrives. Assuming stationarity, Luckock showed that the distribution functions of the best buy and sell order in the order book solve a differential equation, from which he was able to calculate the position of two prices Jc−<Jc+ such that buy orders below Jc− and sell orders above Jc+ stay in the order book forever while all other orders are eventually matched. We extend Luckock’s model by adding market orders, that is, with a certain rate traders arrive at the market that take the best available buy or sell offer in the order book, if there is one, and do nothing otherwise. We give necessary and sufficient conditions for such an extended model to be positive recurrent and show how these conditions are related to the prices Jc− and Jc+ of Luckock. Pracoviště Ústav teorie informace a automatizace Kontakt Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Rok sběru 2019
Počet záznamů: 1