Single- and multiplayer trade execution strategies under transient price impact
Strehle, Elias
URL:
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https://ub-madoc.bib.uni-mannheim.de/43864
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URN:
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urn:nbn:de:bsz:180-madoc-438641
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Document Type:
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Doctoral dissertation
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Year of publication:
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2017
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Place of publication:
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Mannheim
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University:
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Universität Mannheim
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Evaluator:
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Schied, Alexander
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Date of oral examination:
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21 December 2017
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Publication language:
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English
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Institution:
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School of Business Informatics and Mathematics > Wirtschaftsmathematik I (Schied)
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Subject:
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510 Mathematics
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Subject headings (SWD):
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Finanzmathematik , Nash-Gleichgewicht , Transaktionskosten , Wertpapierhandel , Fredholm-Integralgleichung , Schwachsinguläre Fredholm-Integralgleichung , Hochfrequenzhandel
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Keywords (English):
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Financial Mathematics , Nash Equilibrium , Transaction Costs , Fredholm Integral Equations , Market Microstructure , Price Impact , High Frequency Trading , Order Anticipation Strategies , Predatory Trading
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Abstract:
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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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| Dieser Eintrag ist Teil der Universitätsbibliographie. |
| Das Dokument wird vom Publikationsserver der Universitätsbibliothek Mannheim bereitgestellt. |
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