A Markov Model of a Limit Order Book: Thresholds, Recurrence, and Trading Strategies

References

• Adan I, Weiss G (2012) Exact FCFS matching rates for two infinite multitype sequences. Oper. Res. 60(2):475–489.Link, Google Scholar
• Bramson M (2006) Stability and Heavy Traffic Limits for Queueing Networks: St. Flour Lectures Notes (Springer, Berlin).Google Scholar
• Budish E, Cramton P, Shim J (2015) The high-frequency trading arms race: Frequent batch auctions as a market design response. Quart. J. Econom. 130(4):1547–1621.Crossref, Google Scholar
• Budish E, Cramton P, Shim J (2014) Implementation details for frequent batch auctions: Slowing down markets to the blink of an eye. Amer. Econom. Rev. 104(5):418–424.Crossref, Google Scholar
• Cont R, de Larrard A (2013) Price dynamics in a Markovian limit order book market. SIAM J. Financial Math. 4(1):1–25.Crossref, Google Scholar
• Cont R, Stoikov S, Talreja R (2010) A stochastic model for order book dynamics. Oper. Res. 58(3):549–563.Link, Google Scholar
• Duffie D, Zhu H (2017) Size discovery. Rev. Financial Studies 30(4):1095–1150.Google Scholar
• Easley D, de Prado ML, O’Hara M (2012) The volume clock: Insights into the high frequency paradigm. J. Portfolio Management 39:19–29.Crossref, Google Scholar
• Gamarnik D, Katz D (2014) The stability of the deterministic Skorokhod problem is undecidable. Queueing Systems 78(1):1–29.Google Scholar
• Gao X, Deng S (2016) Hydrodynamic limit of order book dynamics. Probab. Engrg. Inform. Sci., ePub ahead of print November 28, https://doi.org/10.1017/S0269964816000413.Crossref, Google Scholar
• Gould MD, Porter MA, Williams S, McDonald M, Fenn DJ, Howison SD (2013) Limit order books. Quant. Finance 13(11):1709–1742.Crossref, Google Scholar
• Kendall D (1951) Some problems in the theory of queues. J. Roy. Statist. Soc. 13(2):151–185.Google Scholar
• Lachapelle A, Lasry J-M, Lehalle C-A, Lions P-L (2014) Efficiency of the price formation process in presence of high frequency participants: A mean field game analysis. Preprint arXiv:1305.6323v3.Google Scholar
• Lakner P, Reed J, Simatos F (2013) Scaling limit of a limit order book model via the regenerative characterization of Lévy trees. Preprint arXiv:1312.2340.Google Scholar
• Lakner P, Reed J, Stoikov S (2016) High frequency asymptotics for the limit order book. Market Microstructure Liquidity 2(1):1650004.Crossref, Google Scholar
• Luckock H (2003) A steady-state model of the continuous double auction. Quant. Finance 3(5):385–404.Crossref, Google Scholar
• Maglaras C, Moallemi CC, Zheng H (2014) Queueing dynamics and state space collapse in fragmented limit order book markets. Columbia Business School Research Paper 14–13.Google Scholar
• Meyn S, Tweedie RL (2009) Markov Chains and Stochastic Stability, 2nd ed. (Cambridge University Press, New York).Crossref, Google Scholar
• Plačková J (2011) Shluky volatility a dynamika poptávky a nabídky. Master’s Thesis, MFF, Charles University Prague (In Czech).Google Scholar
• Roşu I (2009) A dynamic model of the limit order book. Rev. Financial Stud. 22(11):4601–4641.Crossref, Google Scholar
• Simatos F (2014) Coupling limit order books and branching random walks. J. Appl. Probab. 51(3):625–639.Crossref, Google Scholar
• Stigler G (1964) Public regulation of the securities markets. J. Bus. 37(2):117–142.Crossref, Google Scholar
• Stolyar AL, Yudovina E (2013) Systems with large flexible server pools: Instability of “natural” load balancing. Ann. Appl. Probab. 23(5):2099–2138.Crossref, Google Scholar
• Swart J (2016) Rigorous results for the Stigler-Luckock model for the evolution of an order book. Preprint arXiv: 1605.01551.Google Scholar
• Toke M (2015) The order book as a queueing system: Average depth and influence of the size of limit orders. Quant. Finance 15(5):795–808.Crossref, Google Scholar
• Yudovina E (2012) Collaborating queues: Large service network and a limit order book. PhD thesis, University of Cambridge, Cambridge, UK.Google Scholar
• Zenios SA, Chertow GM, Wein LM (2000) Dynamic allocation of kidneys to candidates on the transplant waiting list. Oper. Res. 48(4):549–569.Link, Google Scholar