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Utility maximisation in a factor model with constant and proportional transaction costs

Author

Listed:
  • Christoph Belak

    (University of Trier)

  • Sören Christensen

    (University of Hamburg)

Abstract

We study the problem of maximising expected utility of terminal wealth under constant and proportional transaction costs in a multidimensional market with prices driven by a factor process. We show that the value function is the unique viscosity solution of the associated quasi-variational inequalities and construct optimal strategies. While the value function turns out to be truly discontinuous, we are able to establish a comparison principle for discontinuous viscosity solutions which is strong enough to argue that the value function is unique, globally upper semicontinuous, and continuous if restricted to either borrowing or non-borrowing portfolios.

Suggested Citation

  • Christoph Belak & Sören Christensen, 2019. "Utility maximisation in a factor model with constant and proportional transaction costs," Finance and Stochastics, Springer, vol. 23(1), pages 29-96, January.
    • Handle: RePEc:spr:finsto:v:23:y:2019:i:1:d:10.1007_s00780-018-00380-1
    DOI: 10.1007/s00780-018-00380-1
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    References listed on IDEAS

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    1. Albert Altarovici & Johannes Muhle-Karbe & Halil Soner, 2015. "Asymptotics for fixed transaction costs," Finance and Stochastics, Springer, vol. 19(2), pages 363-414, April.
    2. Christensen, Sören, 2014. "On the solution of general impulse control problems using superharmonic functions," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 709-729.
    3. Seydel, Roland C., 2009. "Existence and uniqueness of viscosity solutions for QVI associated with impulse control of jump-diffusions," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3719-3748, October.
    4. Ralf Korn, 1998. "Portfolio optimisation with strictly positive transaction costs and impulse control," Finance and Stochastics, Springer, vol. 2(2), pages 85-114.
    5. repec:bla:jfinan:v:59:y:2004:i:1:p:289-338 is not listed on IDEAS
    6. Jerome F. Eastham & Kevin J. Hastings, 1988. "Optimal Impulse Control of Portfolios," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 588-605, November.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Christoph Belak & Lukas Mich & Frank T. Seifried, 2019. "Optimal Investment for Retail Investors with Flooredand Capped Costs," Working Paper Series 2019-06, University of Trier, Research Group Quantitative Finance and Risk Analysis.
    2. Soren Christensen & Berenice Anne Neumann & Tobias Sohr, 2020. "Competition versus Cooperation: A class of solvable mean field impulse control problems," Papers 2010.06452, arXiv.org, revised Apr 2021.
    3. Christensen, Sören & Sohr, Tobias, 2020. "A solution technique for Lévy driven long term average impulse control problems," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7303-7337.
    4. Christoph Belak & Lukas Mich & Frank T. Seifried, 2022. "Optimal investment for retail investors," Mathematical Finance, Wiley Blackwell, vol. 32(2), pages 555-594, April.
    5. Luciano Campi & Davide Santis, 2020. "Nonzero-Sum Stochastic Differential Games Between an Impulse Controller and a Stopper," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 688-724, August.
    6. Lin He & Zongxia Liang & Sheng Wang, 2022. "Modern Tontine with Transaction Costs," Papers 2209.09709, arXiv.org, revised Jun 2023.

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    More about this item

    Keywords

    Portfolio optimisation; Transaction costs; Discontinuous viscosity solutions; Comparison principle; Stochastic Perron method;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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