Single- and multiplayer trade execution strategies under transient price impact

Strehle, Elias

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URN: urn:nbn:de:bsz:180-madoc-438641
Document Type: Doctoral dissertation
Year of publication: 2017
Place of publication: Mannheim
University: Universität Mannheim
Evaluator: Schied, Alexander
Date of oral examination: 21 December 2017
Publication language: English
Institution: School of Business Informatics and Mathematics > Wirtschaftsmathematik I (Schied)
Subject: 510 Mathematics
Subject headings (SWD): Finanzmathematik , Nash-Gleichgewicht , Transaktionskosten , Wertpapierhandel , Fredholm-Integralgleichung , Schwachsinguläre Fredholm-Integralgleichung , Hochfrequenzhandel
Keywords (English): 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.

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