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Optimal portfolio policies under fixed and proportional transaction costs

Part of: Stochastic systems and control Miscellaneous topics in calculus of variations and optimal control

Published online by Cambridge University Press:  08 September 2016

Albrecht Irle  and
Jörn Sass
Albrecht Irle*
Affiliation:
University of Kiel
Jörn Sass*
Affiliation:
Austrian Academy of Sciences
*
∗ Postal address: Mathematisches Seminar, University of Kiel, Ludwig-Meyn-Strasse 4, D-24098 Kiel, Germany. Email address: irle@math.uni-kiel.de
∗∗ Postal address: RICAM, Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria. Email address: joern.sass@oeaw.ac.at
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Abstract

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We consider the portfolio optimization problem of maximizing the asymptotic growth rate under a combination of fixed and proportional costs. Expressing the asymptotic growth rate in terms of the risky fraction process, the problem can be transformed to that of controlling a diffusion in one dimension. Then we use the corresponding quasivariational inequalities to obtain the explicit shape together with the existence of an optimal impulse control strategy. This optimal strategy is given by only four parameters: two for the stopping boundaries and two for the new risky fractions the investor chooses at these times.

Keywords

Asymptotic growth rateimpulse controlfixed costproportional costportfolio optimizationtransaction cost

MSC classification

Secondary: 49N25: Impulsive optimal control problems 93E20: Optimal stochastic control
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 38 , Issue 4 , December 2006 , pp. 916 - 942
Copyright
Copyright © Applied Probability Trust 2006 

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