Order Book Resilience, Price Manipulation and the Positive Portfolio Problem

Alfonsi, Aurélien ; Schied, Alexander ; Slynko, Alla

DOI: https://doi.org/10.1137/110822098
URL: http://epubs.siam.org/doi/pdf/10.1137/110822098
Document Type: Article
Year of publication: 2012
The title of a journal, publication series: SIAM Journal on Financial Mathematics : SIFIN
Volume: 3
Issue number: 1
Page range: 511-533
Place of publication: Philadelphia, Pa.
Publishing house: SIAM
ISSN: 1945-497X
Publication language: English
Institution: School of Business Informatics and Mathematics > Wirtschaftsmathematik I (Schied)
Subject: 510 Mathematics
Abstract: The viability of a market impact model is usually considered to be equivalent to the absence of price manipulation strategies in the sense of Huberman & Stanzl (2004). 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 decreasing 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.

Dieser Eintrag ist Teil der Universitätsbibliographie.

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