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Optimal portfolio policies under fixed and proportional transaction costs

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

References

Akian, M., Menaldi, J. L. and Sulem, A. (1996). On an investment–consumption model with transaction costs. SIAM J. Control Optimization 34, 329–364.CrossRefGoogle Scholar
Akian, M., Sulem, A. and Taksar, M. I. (2001). Dynamic optimization of long-term growth rate for a portfolio with transaction costs and logarithmic utility. Math. Finance 11, 153–188.CrossRefGoogle Scholar
Bielecki, T. R. and Pliska, S. R. (2000). Risk sensitive asset management with transaction costs. Finance Stoch. 4, 1–33.CrossRefGoogle Scholar
Davis, M. H. A. and Norman, A. R. (1990). Portfolio selection with transaction costs. Math. Operat. Res. 15, 676–713.CrossRefGoogle Scholar
Eastham, J. F. and Hastings, K. J. (1988). Optimal impulse control of portfolios. Math. Operat. Res. 13, 588–605.CrossRefGoogle Scholar
Irle, A. and Sass, J. (2005). Good portfolio strategies under transaction costs: a renewal theoretic approach. In Stochastic Finance, eds do Rosario Grossinho, M., Shiryaev, A. N., Esquivel, M. L. and Oliveira, P. E., Springer, New York, pp. 321–341.Google Scholar
Jack, A. and Zervos, M. (2005). Impulse control of one-dimensional Itô diffusions with an expected and a pathwise ergodic criterion. Preprint. Available at http://www.mth.kcl.ac.uk/finmath/articles/Jack-Zervos-IC.pdf.Google Scholar
Kabanov, Y. and Klüppelberg, C. (2004). A geometric approach to portfolio optimization in models with transaction costs. Finance Stoch. 8, 207–227.CrossRefGoogle Scholar
Korn, R. (1998). Portfolio optimisation with strictly positive transaction costs and impulse control. Finance Stoch. 2, 85–114.CrossRefGoogle Scholar
Korn, R. (2004). Realism and practicality of transaction cost approaches in continuous-time portfolio optimisation: the scope of the Morton–Pliska approach. Math. Meth. Operat. Res. 60, 165–174.CrossRefGoogle Scholar
Magill, M. J. P. and Constantinides, G. M. (1976). Portfolio selection with transaction costs. J. Econom. Theory 13, 245–263.CrossRefGoogle Scholar
Merton, R. C. (1969). Lifetime portfolio selection under uncertainty: the continuous-time case. Rev. Econom. Statist. 51, 247–257.CrossRefGoogle Scholar
Morton, A. J. and Pliska, S. R. (1995). Optimal portfolio management with fixed transaction costs. Math. Finance 5, 337–356.CrossRefGoogle Scholar
Øksendal, B. and Sulem, A. (2001). Optimal consumption and portfolio with both fixed and proportional transaction costs. SIAM J. Control Optimization 40, 1765–1790.CrossRefGoogle Scholar
Sass, J. (2005). Portfolio optimization under transaction costs in the CRR model. Math. Meth. Operat. Res. 61, 239–259.CrossRefGoogle Scholar
Shreve, S. E. and Soner, H. M. (1994). Optimal investment and consumption with transaction costs. Ann. Appl. Prob. 4, 609–692.CrossRefGoogle Scholar
Sulem, A. (1997). Dynamic optimization for a mixed portfolio with transaction costs. In Numerical Methods in Finance, eds Rogers, L. C. G. and Talay, D., Cambridge University Press, pp. 165–180.CrossRefGoogle Scholar
Taksar, M., Klass, M. J. and Assaf, D. (1988). A diffusion model for optimal portfolio selection in the presence of brokerage fees. Math. Operat. Res. 13, 277–294.CrossRefGoogle Scholar