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Primal-dual methods for the computation of trading regions under proportional transaction costs

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  • Roland Herzog
  • Karl Kunisch
  • Jörn Sass

Abstract

Portfolio optimization problems on a finite time horizon under proportional transaction costs are considered. The objective is to maximize the expected utility of the terminal wealth. The ensuing non-smooth time-dependent Hamilton–Jacobi–Bellman equation is solved by regularization and the application of a semi-smooth Newton method. Discretization in space is carried out by finite differences or finite elements. Computational results for one and two risky assets are provided. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Roland Herzog & Karl Kunisch & Jörn Sass, 2013. "Primal-dual methods for the computation of trading regions under proportional transaction costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(1), pages 101-130, February.
    • Handle: RePEc:spr:mathme:v:77:y:2013:i:1:p:101-130
    DOI: 10.1007/s00186-012-0416-3
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    References listed on IDEAS

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    1. Muthuraman, Kumar, 2007. "A computational scheme for optimal investment - consumption with proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1132-1159, April.
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    5. Karl Kunisch & Jörn Sass, 2007. "Trading Regions Under Proportional Transaction Costs," Operations Research Proceedings, in: Karl-Heinz Waldmann & Ulrike M. Stocker (ed.), Operations Research Proceedings 2006, pages 563-568, Springer.
    6. Valeri Zakamouline, 2005. "A unified approach to portfolio optimization with linear transaction costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(2), pages 319-343, November.
    7. W. Li & S. Wang, 2009. "Penalty Approach to the HJB Equation Arising in European Stock Option Pricing with Proportional Transaction Costs," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 279-293, November.
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    Cited by:

    1. Yoshioka, Hidekazu & Yaegashi, Yuta, 2019. "A finite difference scheme for variational inequalities arising in stochastic control problems with several singular control variables," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 40-66.
    2. Palczewski, Jan & Poulsen, Rolf & Schenk-Hoppé, Klaus Reiner & Wang, Huamao, 2015. "Dynamic portfolio optimization with transaction costs and state-dependent drift," European Journal of Operational Research, Elsevier, vol. 243(3), pages 921-931.
    3. Christoph Belak & Jörn Sass, 2019. "Finite-horizon optimal investment with transaction costs: construction of the optimal strategies," Finance and Stochastics, Springer, vol. 23(4), pages 861-888, October.

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