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Optimal investment under capital gains taxes

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Listed:
  • Alexander Dimitrov
  • Christoph Kuhn

Abstract

We generalize classical results on the existence of optimal portfolios in discrete time frictionless market models to models with capital gains taxes. We consider the realistic but mathematically challenging rule that losses do not trigger negative taxes but can only be offset against potential gains in the future. Central to the analysis is a well-known phenomenon from arbitrage-free markets with proportional transaction costs that does not exist in arbitrage-free frictionless markets: an investment in specific quantities of stocks that is completely riskless but may provide an advantage over holding money in the bank account. As a result of this phenomenon, on an infinite probability space, no-arbitrage does not imply that the set of attainable terminal wealth is closed in probability. We show closedness under the slightly stronger {\em no unbounded non-substitutable investment with bounded risk} condition. As a by-product, we provide a proof that in discrete time frictionless models with short-selling constraints, no-arbitrage implies that the set of attainable terminal wealth is closed in probability -- even if there are redundant stocks.

Suggested Citation

  • Alexander Dimitrov & Christoph Kuhn, 2026. "Optimal investment under capital gains taxes," Papers 2602.15177, arXiv.org.
    • Handle: RePEc:arx:papers:2602.15177
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    References listed on IDEAS

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    1. Constantinides, George M, 1983. "Capital Market Equilibrium with Personal Tax," Econometrica, Econometric Society, vol. 51(3), pages 611-636, May.
    2. 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.
    3. 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.
    4. repec:dau:papers:123456789/5607 is not listed on IDEAS
    5. 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.
    6. repec:dau:papers:123456789/5600 is not listed on IDEAS
    7. Imen Ben Tahar & Nizar Touzi & Mete H. Soner, 2010. "Merton Problem with Taxes: Characterization, computation and Approximation," Post-Print hal-00703102, HAL.
    8. Christoph Kuhn & Alexander Molitor, 2018. "Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costs," Papers 1811.11621, arXiv.org, revised Apr 2019.
    9. Schachermayer, W., 1992. "A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 249-257, December.
    10. Paul Ehling & Michael Gallmeyer & Sanjay Srivastava & Stathis Tompaidis & Chunyu Yang, 2018. "Portfolio Tax Trading with Carryover Losses," Management Science, INFORMS, vol. 64(9), pages 4156-4176, September.
    11. repec:bla:jfinan:v:59:y:2004:i:3:p:999-1037 is not listed on IDEAS
    12. Elyès Jouini & Pf. Koehl & Nizar Touzi, 1997. "Optimal Investment with Taxes : An Optimal Control Problem with Endogenous Delay," Working Papers 97-44, Center for Research in Economics and Statistics.
    13. Walter Schachermayer, 2004. "The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 19-48, January.
    14. repec:dau:papers:123456789/9561 is not listed on IDEAS
    15. Jan Kallsen & Johannes Muhle-Karbe, 2011. "Existence of shadow prices in finite probability spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(2), pages 251-262, April.
    16. Jouini, Elyes & Koehl, Pierre-F. & Touzi, Nizar, 2000. "Optimal investment with taxes: an existence result," Journal of Mathematical Economics, Elsevier, vol. 33(4), pages 373-388, May.
    17. 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.
    18. Martin Haugh & Garud Iyengar & Chun Wang, 2016. "Tax-Aware Dynamic Asset Allocation," Operations Research, INFORMS, vol. 64(4), pages 849-866, August.
    19. Dammon, Robert M & Spatt, Chester S & Zhang, Harold H, 2001. "Optimal Consumption and Investment with Capital Gains Taxes," The Review of Financial Studies, Society for Financial Studies, vol. 14(3), pages 583-616.
    20. repec:oup:rfinst:v:21:y:2017:i:5:p:1847-1873. is not listed on IDEAS
    21. Marcel Fischer & Michael Gallmeyer, 2017. "Taxable and Tax-Deferred Investing with the Limited Use of Losses," Review of Finance, European Finance Association, vol. 21(5), pages 1847-1873.
    22. Christoph Kühn & Alexander Molitor, 2019. "Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costs," Finance and Stochastics, Springer, vol. 23(4), pages 1049-1077, October.
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