A dynamic model of the limit order book

Alberto Bressan, Marco Mazzola, Hongxu Wei

Research output: Contribution to journalArticlepeer-review


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
Issue number3
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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