Probabilistic properties of the continuous double auction.

*(English)*Zbl 1298.91093The 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.

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.

Reviewer: Tamás Mátrai (Budapest)

##### MSC:

91B26 | Auctions, bargaining, bidding and selling, and other market models |

91G80 | Financial applications of other theories |

**OpenURL**

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