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Mathematics and Financial Economics

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26-07-2016

Optimal placement in a limit order book: an analytical approach

Authors: Xin Guo, Adrien de Larrard, Zhao Ruan

Published in: Mathematics and Financial Economics | Issue 2/2017

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Abstract

This paper proposes and studies an optimal placement problem in a limit order book. Under a correlated random walk model with mean-reversion for the best ask/bid price, optimal placement strategies for both static and dynamic cases are derived. In the static case, the optimal strategy involves only the market order, the best bid, and the second best bid; the optimal strategy for the dynamic case is shown to be of a threshold type depending on the remaining trading time, the market momentum, and the price mean-reversion factor. Critical to the analysis is a generalized reflection principle for correlated random walks, which enables a significant dimension reduction.

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This rebate structure varies from exchange to exchange and leads to different optimization problems. In some exchanges successful executions of limit orders get a discount (i.e., a fixed percentage of the execution price) whereas in other places the discount may be a fixed amount.

Literature on the optimal execution problem is big and growing rapidly fast, see for instance, Bertsimas and Lo [12], Almgren and Chriss [5, 6], Almgren [4], Almgren and Lorenz [7], Schied and Schöneborn [48], Weiss [51], Alfonsi et al. [2, 3], Predoiu et al. [44], Schied et al. [49], Gatheral and Schied [24], Forsyth et al. [23], Bouchard et al. [13], Obizhaeva and Wang [43], and most recently Becherer et al. [11], Horst et al. [40], Cheridito and Sepin [19], Guo and Zervos [29], Huitema [35], Kratz [38], and Moallemi and Yuan [41].

Clearly, in practice, traders may change their strategies without any price change; also the clock for the price movement in general differs from the usual time clock. Adding these features would be worthy future research topics.

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Title: Optimal placement in a limit order book: an analytical approach
Authors: Xin Guo
Adrien de Larrard
Zhao Ruan
Publication date: 26-07-2016
Publisher: Springer Berlin Heidelberg
Published in: Mathematics and Financial Economics / Issue 2/2017
Print ISSN: 1862-9679
Electronic ISSN: 1862-9660
DOI: https://doi.org/10.1007/s11579-016-0177-5

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