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Trading with small nonlinear price impact
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Cayé, Thomas, Herdegen, Martin and Muhle-Karbe, Johannes (2020) Trading with small nonlinear price impact. Annals of Applied Probability, 30 (2). pp. 706-746. doi:10.1214/19-AAP1513 ISSN 1050-5164.
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Official URL: http://dx.doi.org/10.1214/19-AAP1513
Abstract
We study portfolio choice with small nonlinear price impact on general market dynamics. Using probabilistic techniques and convex duality, we show that the asymptotic optimum can be described explicitly up to the solution of a nonlinear ODE, which identifies the optimal trading speed and the performance loss due to the trading friction. Previous asymptotic results for proportional and quadratic trading costs are obtained as limiting cases. As an illustration, we discuss how nonlinear trading costs affect the pricing and hedging of derivative securities and active portfolio management.
Item Type: | Journal Article | |||||||||
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Subjects: | H Social Sciences > HG Finance Q Science > QA Mathematics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||
Library of Congress Subject Headings (LCSH): | Pricing -- Mathematical models, Options (Finance) -- Mathematical models, Differential equations, Partial, Nonlinear pricing -- Mathematical models | |||||||||
Journal or Publication Title: | Annals of Applied Probability | |||||||||
Publisher: | Institute of Mathematical Statistics | |||||||||
ISSN: | 1050-5164 | |||||||||
Official Date: | 2020 | |||||||||
Dates: |
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Volume: | 30 | |||||||||
Number: | 2 | |||||||||
Page Range: | pp. 706-746 | |||||||||
DOI: | 10.1214/19-AAP1513 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Date of first compliant deposit: | 18 July 2019 | |||||||||
Date of first compliant Open Access: | 6 October 2020 | |||||||||
RIOXX Funder/Project Grant: |
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