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

Author

Listed:
  • Alfonsi Aurélien

    (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

    (Department of Mathematics - Universität Mannheim)

  • Alla Slynko

    (Department of Mathematics - Universität Mannheim)

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.

Suggested Citation

  • Alfonsi Aurélien & Alexander Schied & Alla Slynko, 2012. "Order Book Resilience, Price Manipulation, and the Positive Portfolio Problem," Post-Print hal-00941333, HAL.
    • Handle: RePEc:hal:journl:hal-00941333
    DOI: 10.1137/110822098
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