Single- and multiplayer trade execution strategies under transient price impact

Strehle, Elias

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URL:	https://ub-madoc.bib.uni-mannheim.de/43864
URN:	urn:nbn:de:bsz:180-madoc-438641
Dokumenttyp:	Dissertation
Erscheinungsjahr:	2017
Ort der Veröffentlichung:	Mannheim
Hochschule:	Universität Mannheim
Gutachter:	Schied, Alexander
Datum der mündl. Prüfung:	21 Dezember 2017
Sprache der Veröffentlichung:	Englisch
Einrichtung:	Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik > Wirtschaftsmathematik I (Schied)
Fachgebiet:	510 Mathematik
Normierte Schlagwörter (SWD):	Finanzmathematik , Nash-Gleichgewicht , Transaktionskosten , Wertpapierhandel , Fredholm-Integralgleichung , Schwachsinguläre Fredholm-Integralgleichung , Hochfrequenzhandel
Freie Schlagwörter (Englisch):	Financial Mathematics , Nash Equilibrium , Transaction Costs , Fredholm Integral Equations , Market Microstructure , Price Impact , High Frequency Trading , Order Anticipation Strategies , Predatory Trading
Abstract:	The problem of optimal execution is to trade a fixed amount of a financial asset over a fixed time horizon in a way that minimizes costs from price impact and transaction costs. Three types of price impact can be distinguished: Temporary, transient and permanent price impact. While mathematical models of optimal execution under temporary and permanent price impact can be analyzed with standard methods from the calculus of variations, models featuring transient price impact are more complex. This thesis studies optimal execution under transient price impact for a single investor and for multiple investors. Assuming that trading incurs quadratic transaction costs, existence and uniqueness of optimal execution strategies and Nash equilibria is established for a large class of transient price impact functions. Closed-form representations of Nash equilibria are derived under the assumption that price impact decays exponentially. These representations are studied in detail to arrive at an economic evaluation of order anticipation strategies and predatory trading. A second focus of this thesis is the intimate connection between problems of optimal execution and Fredholm integral equations. It is shown that, given information about certain characteristics of transient price impact, one can deduce qualitative features of optimal execution strategies, such as nonnegativity and convexity, from the corresponding Fredholm integral equations without obtaining an explicit solution.