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The Dynamic Programming Equation for the Problem of Optimal Investment Under Capital Gains Taxes

Author

Listed:
  • Imen Ben Tahar

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Nizar Touzi

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Mete H. Soner

    (D-MATH - Department of Mathematics [ETH Zurich] - ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich])

Abstract

This paper considers an extension of the Merton optimal investment problem to the case where the risky asset is subject to transaction costs and capital gains taxes. We derive the dynamic programming equation in the sense of constrained viscosity solutions. We next introduce a family of functions $(V_\varepsilon)_{\varepsilon>0}$, which converges to our value function uniformly on compact subsets, and which is characterized as the unique constrained viscosity solution of an approximation of our dynamic programming equation.

Suggested Citation

  • Imen Ben Tahar & Nizar Touzi & Mete H. Soner, 2007. "The Dynamic Programming Equation for the Problem of Optimal Investment Under Capital Gains Taxes," Post-Print hal-00703103, HAL.
    • Handle: RePEc:hal:journl:hal-00703103
    DOI: 10.1137/050646044
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    Citations

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    Cited by:

    1. Christoph Kuhn & Bjorn Ulbricht, 2013. "Modeling capital gains taxes for trading strategies of infinite variation," Papers 1309.7368, arXiv.org, revised Jun 2015.
    2. Yaoting Lei & Ya Li & Jing Xu, 2020. "Two Birds, One Stone: Joint Timing of Returns and Capital Gains Taxes," Management Science, INFORMS, vol. 66(2), pages 823-843, February.
    3. Olivier Menoukeu-Pamen & Ludovic Tangpi, 2023. "Maximum Principle for Stochastic Control of SDEs with Measurable Drifts," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1195-1228, June.
    4. Christoph Kuhn, 2018. "How local in time is the no-arbitrage property under capital gains taxes ?," Papers 1802.06386, arXiv.org, revised Sep 2018.
    5. Christoph Kuhn & Budhi Arta Surya & Bjorn Ulbricht, 2014. "Optimal Selling Time of a Stock under Capital Gains Taxes," Papers 1501.00026, arXiv.org.
    6. Baojun Bian & Xinfu Chen & Min Dai & Shuaijie Qian, 2021. "Penalty method for portfolio selection with capital gains tax," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 1013-1055, July.
    7. Frank Seifried, 2010. "Optimal investment with deferred capital gains taxes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 181-199, February.
    8. Jiatu Cai & Xinfu Chen & Min Dai, 2018. "Portfolio Selection with Capital Gains Tax, Recursive Utility, and Regime Switching," Management Science, INFORMS, vol. 64(5), pages 2308-2324, May.

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