Translator Disclaimer
April 2020 Trading with small nonlinear price impact
Thomas Cayé, Martin Herdegen, Johannes Muhle-Karbe
Ann. Appl. Probab. 30(2): 706-746 (April 2020). DOI: 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.

Citation

Download Citation

Thomas Cayé. Martin Herdegen. Johannes Muhle-Karbe. "Trading with small nonlinear price impact." Ann. Appl. Probab. 30 (2) 706 - 746, April 2020. https://doi.org/10.1214/19-AAP1513

Information

Received: 1 July 2018; Revised: 1 March 2019; Published: April 2020
First available in Project Euclid: 8 June 2020

zbMATH: 07236132
MathSciNet: MR4108120
Digital Object Identifier: 10.1214/19-AAP1513

Subjects:
Primary: 91G10, 91G80

Rights: Copyright © 2020 Institute of Mathematical Statistics

JOURNAL ARTICLE
41 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.30 • No. 2 • April 2020
Back to Top