Order Book Resilience, Price Manipulation, and the Positive Portfolio Problem
Université Paris Est - CERMICS
University of Mannheim
Technische Universität München (TUM)
August 22, 2012
SIAM Journal on Financial Mathematics, Forthcoming
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.
Number of Pages in PDF File: 24
Keywords: Transient price impact, market impact model, optimal order execution, price manipulation, transaction-triggered price manipulation, Bochner form, positive definite function, no short sales in Markowitz portfolio
JEL Classification: G12, G32
Date posted: November 4, 2009 ; Last revised: April 2, 2012
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