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Optimal portfolio selection under vanishing fixed transaction costs

Part of: Stochastic systems and control Mathematical finance

Published online by Cambridge University Press:  17 November 2017

Sören Christensen ,
Albrecht Irle  and
Andreas Ludwig
Sören Christensen*
Affiliation:
Hamburg University
Albrecht Irle*
Affiliation:
Christian-Albrechts-University Kiel
Andreas Ludwig*
Affiliation:
Christian-Albrechts-University Kiel
*
* Postal address: Department of Mathematics, Hamburg University, SPST, Bundesstraße 55, 20146 Hamburg, Germany. Email address: soeren.christensen@uni-hamburg.de
** Postal address: Mathematisches Seminar, Christian-Albrechts-University Kiel, Ludewig-Meyn-Str. 4, D-24098 Kiel, Germany.
** Postal address: Mathematisches Seminar, Christian-Albrechts-University Kiel, Ludewig-Meyn-Str. 4, D-24098 Kiel, Germany.
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Abstract

In this paper asymptotic results in a long-term growth rate portfolio optimization model under both fixed and proportional transaction costs are obtained. More precisely, the convergence of the model when the fixed costs tend to 0 is investigated. A suitable limit model with purely proportional costs is introduced and the convergence of optimal boundaries, asymptotic growth rates, and optimal risky fraction processes is rigorously proved. The results are based on an in-depth analysis of the convergence of the solutions to the corresponding Hamilton–Jacobi–Bellman equations.

Keywords

Impulse controlHunt processesthreshold ruleexcessive function

MSC classification

Primary: 91G10: Portfolio theory
Secondary: 93E20: Optimal stochastic control
Type
Research Article
Information
Advances in Applied Probability , Volume 49 , Issue 4 , December 2017 , pp. 1116 - 1143
Copyright
Copyright © Applied Probability Trust 2017 

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