Order Book Resilience, Price Manipulation, and the Positive Portfolio Problem

Alfonsi Aurélien (), Alexander Schied and Alla Slynko
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Alfonsi Aurélien: CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées, 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 nationale des ponts et chaussées
Alexander Schied: Department of Mathematics - University of Mannheim = Universität Mannheim
Alla Slynko: Department of Mathematics - University of Mannheim = Universität Mannheim

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Abstract: The viability of a market impact model is usually considered to be equivalent to the absence of price manipulation strategies. By analyzing a model with linear instantaneous, transient, and permanent impact components, we discover a new class of irregularities, which we call transaction-triggered price manipulation strategies. We prove that price impact must decay as a convex nonincreasing function of time to exclude these market irregularities along with standard price manipulation. This result is based on a mathematical theorem on the positivity of minimizers of a quadratic form under a linear constraint, which is in turn related to the problem of excluding the existence of short sales in an optimal Markowitz portfolio.

Date: 2012
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Published in SIAM Journal on Financial Mathematics, 2012, 3, pp.511-533. ⟨10.1137/110822098⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00941333

DOI: 10.1137/110822098

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