Optimal trade execution and absence of price manipulations in limit order book models

Aurélien Alfonsi () and Alexander Schied
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Aurélien Alfonsi: CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École des Ponts ParisTech, MATHRISK - Mathematical Risk handling - Inria Paris-Rocquencourt - Inria - Institut National de Recherche en Informatique et en Automatique - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École des Ponts ParisTech
Alexander Schied: Institute of Mathematics - Universität Mannheim

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Abstract: We analyze the existence of price manipulation and optimal trade execution strategies in a model for an electronic limit order book with nonlinear price impact and exponential resilience. Our main results show that, under general conditions on the shape function of the limit order book, placing deterministic trade sizes at trading dates that are homogeneously spaced is optimal within a large class of adaptive strategies with arbitrary trading dates. This extends results from our earlier work with A. Fruth. Perhaps even more importantly, our analysis yields as a corollary that our model does not admit price manipulation strategies. This latter result contrasts the recent findings of Gatheral [12], where, in a related but different model, exponential resilience was found to give rise to price manipulation strategies when price impact is nonlinear.

Date: 2010
Note: View the original document on HAL open archive server: https://hal.science/hal-00397652v3
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Published in SIAM Journal on Financial Mathematics, 2010, 1, pp.490-522. ⟨10.1137/090762786⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00397652

DOI: 10.1137/090762786

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