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Probabilistic properties of the continuous double auction. (English) Zbl 1298.91093
The author formulates a general model of the continuous double auction, i.e. a market where agents can put/cancel limit orders or put market orders at any instant during the trading hours. This provides a unified framework of the models discussed by H. Luckock [“A steady-state model of the continuous double auction”, Quant. Finance 3, No. 5, 385–404 (2003)], S. Maslov [“Simple model of a limit order driven market”, Physica A 278, No. 3–4, 571–578 (2000; doi:10.1016/S0378-4371(00)00067-4)] and E. Smith et al. [“Statistical theory of the continuous double auction”, Quant. Finance 3, No. 6, 481–514 (2003)], opening a way to the simulation and statistical testing of these models.
The setup presented in the paper allows for an arbitrary (satisfying obvious technical assumptions) distribution for the arrival of new orders. As the main result, the author writes up the distribution of the order book and the distribution of the best quotes. The resulting formulate are quite complicated and recursive in nature; nevertheless, a step is taken toward the simulation of the model.

MSC:
91B26 Auctions, bargaining, bidding and selling, and other market models
91G80 Financial applications of other theories
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References:
[1] D. J. Daley, D. Vere-Jones: An Introduction to the Theory of Point Processes. Second edition. Springer, New York 2003. · Zbl 1026.60061
[2] J. Hoffmann-Jørgenson: Probability with a View Towards to Statistics I. Chapman and Hall, New York, 1994.
[3] O. Kallenberg: Foundations of Modern Probability. Second edition. Springer, New York 2002. · Zbl 0996.60001
[4] H. Luckock: A steady-state model of the continuous double auction. Quantitative Finance 3 (2003), 385-404.
[5] S. Maslov: Simple model of a limit order driven market. Physica A 278 (2000), 571-578.
[6] S. Mike, J. D. Farmer: An empirical behavioral model of liquidity and volatility. J. Econom. Dynamics Control 32 (2008), 200-234. · Zbl 05660203
[7] D. Pollard: A User’s Guide to Measure Theoretic Probability. Cambridge Univ. Press, Cambridge 2002. · Zbl 0992.60001
[8] M. Šmíd: On Approximation of Stochastic Programming Problems. PhD Thesis, Charles University, Department of Probability Statistics, 2004.
[9] M. Šmíd: Price tails in the Smith and Farmer’s model. Bull. Czech Econometric Soc. 25 (2008), 31-40.
[10] M. Šmíd: Probabilistic Properties of the Continuous Double Auction. Research Report No. 2304. Institute of Information Theory and Automation, Prague 2011.
[11] E. Smith, J. D. Farmer, L. Gillemot, S. Krishnamurthy: Statistical theory of the continuous double auction. Quantitative Finance 3 (2003), 6, 481-514.
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