Download this Paper Open PDF in Browser

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

SIAM Journal on Financial Mathematics, Forthcoming

24 Pages Posted: 4 Nov 2009 Last revised: 2 Apr 2012

Aurélien Alfonsi

Université Paris Est - CERMICS

Alexander Schied

University of Mannheim

Alla Slynko

Technische Universität München (TUM)

Date Written: August 22, 2012

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.

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

Suggested Citation

Alfonsi, Aurélien and Schied, Alexander and Slynko, Alla, Order Book Resilience, Price Manipulation, and the Positive Portfolio Problem (August 22, 2012). SIAM Journal on Financial Mathematics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1498514 or http://dx.doi.org/10.2139/ssrn.1498514

Aurélien Alfonsi

Université Paris Est - CERMICS ( email )

6 et 8 avenue Blaise Pascal
Marne-la-Vallée, Champs sur marne 77420
France

Alexander Schied (Contact Author)

University of Mannheim ( email )

Department of Mathematics
A 5, 6
Mannheim, 68131
Germany
+49-621-181-2513 (Phone)

HOME PAGE: http://www.alexschied.de/

Alla Slynko

Technische Universität München (TUM) ( email )

Arcisstrasse 21
Munich, 80333
Germany

Paper statistics

Downloads
1,014
Rank
17,190
Abstract Views
3,229