A dynamic model of the limit order book

Alberto Bressan, Marco Mazzola, Hongxu Wei

Research output: Contribution to journalArticle

Abstract

We consider an equilibrium model of the Limit Order Book in a stock market, where a large number of competing agents post “buy” or “sell” orders. For the “one-shot” game, it is shown that the two sides of the LOB are determined by the distribution of the random size of the incoming order, and by the maximum price accepted by external buyers (or the minimum price accepted by external sellers). We then consider an iterated game, where more agents come to the market, posting both market orders and limit orders. Equilibrium strategies are found by backward induction, in terms of a value function which depends on the current sizes of the two portions of the LOB. The existence of a unique Nash equilibrium is proved under a natural assumption, namely: the probability that the external order is so large that it wipes out the entire LOB should be sufficiently small.

Original languageEnglish (US)
Pages (from-to)1015-1041
Number of pages27
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume25
Issue number3
DOIs
StatePublished - Jan 1 2020

Fingerprint

Dynamic models
Dynamic Model
Game
Backward Induction
Equilibrium Model
Stock Market
Nash Equilibrium
Value Function
Entire
Financial markets
Market

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Bressan, Alberto ; Mazzola, Marco ; Wei, Hongxu. / A dynamic model of the limit order book. In: Discrete and Continuous Dynamical Systems - Series B. 2020 ; Vol. 25, No. 3. pp. 1015-1041.
@article{b7f1ec6e55354abf9c7db0a92380989c,
title = "A dynamic model of the limit order book",
abstract = "We consider an equilibrium model of the Limit Order Book in a stock market, where a large number of competing agents post “buy” or “sell” orders. For the “one-shot” game, it is shown that the two sides of the LOB are determined by the distribution of the random size of the incoming order, and by the maximum price accepted by external buyers (or the minimum price accepted by external sellers). We then consider an iterated game, where more agents come to the market, posting both market orders and limit orders. Equilibrium strategies are found by backward induction, in terms of a value function which depends on the current sizes of the two portions of the LOB. The existence of a unique Nash equilibrium is proved under a natural assumption, namely: the probability that the external order is so large that it wipes out the entire LOB should be sufficiently small.",
author = "Alberto Bressan and Marco Mazzola and Hongxu Wei",
year = "2020",
month = "1",
day = "1",
doi = "10.3934/dcdsb.2019206",
language = "English (US)",
volume = "25",
pages = "1015--1041",
journal = "Discrete and Continuous Dynamical Systems - Series B",
issn = "1531-3492",
publisher = "Southwest Missouri State University",
number = "3",

}

A dynamic model of the limit order book. / Bressan, Alberto; Mazzola, Marco; Wei, Hongxu.

In: Discrete and Continuous Dynamical Systems - Series B, Vol. 25, No. 3, 01.01.2020, p. 1015-1041.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A dynamic model of the limit order book

AU - Bressan, Alberto

AU - Mazzola, Marco

AU - Wei, Hongxu

PY - 2020/1/1

Y1 - 2020/1/1

N2 - We consider an equilibrium model of the Limit Order Book in a stock market, where a large number of competing agents post “buy” or “sell” orders. For the “one-shot” game, it is shown that the two sides of the LOB are determined by the distribution of the random size of the incoming order, and by the maximum price accepted by external buyers (or the minimum price accepted by external sellers). We then consider an iterated game, where more agents come to the market, posting both market orders and limit orders. Equilibrium strategies are found by backward induction, in terms of a value function which depends on the current sizes of the two portions of the LOB. The existence of a unique Nash equilibrium is proved under a natural assumption, namely: the probability that the external order is so large that it wipes out the entire LOB should be sufficiently small.

AB - We consider an equilibrium model of the Limit Order Book in a stock market, where a large number of competing agents post “buy” or “sell” orders. For the “one-shot” game, it is shown that the two sides of the LOB are determined by the distribution of the random size of the incoming order, and by the maximum price accepted by external buyers (or the minimum price accepted by external sellers). We then consider an iterated game, where more agents come to the market, posting both market orders and limit orders. Equilibrium strategies are found by backward induction, in terms of a value function which depends on the current sizes of the two portions of the LOB. The existence of a unique Nash equilibrium is proved under a natural assumption, namely: the probability that the external order is so large that it wipes out the entire LOB should be sufficiently small.

UR - http://www.scopus.com/inward/record.url?scp=85076441748&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85076441748&partnerID=8YFLogxK

U2 - 10.3934/dcdsb.2019206

DO - 10.3934/dcdsb.2019206

M3 - Article

AN - SCOPUS:85076441748

VL - 25

SP - 1015

EP - 1041

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

IS - 3

ER -