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Pathwise analysis of log-optimal portfolios

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  • Andrew L. Allan
  • Anna P. Kwossek
  • Chong Liu
  • David J. Promel

Abstract

Based on the theory of c\`adl\`ag rough paths, we develop a pathwise approach to analyze stability and approximation properties of portfolios along individual price trajectories generated by standard models of financial markets. As a prototypical example from portfolio theory, we study the log-optimal portfolio in a classical investment-consumption optimization problem on a frictionless financial market modelled by an It\^o diffusion process. We identify a fully deterministic framework that enables a pathwise construction of the log-optimal portfolio, for which we then establish pathwise stability estimates with respect to the underlying model parameters. We also derive pathwise error estimates arising from the time-discretization of the log-optimal portfolio and its associated capital process.

Suggested Citation

  • Andrew L. Allan & Anna P. Kwossek & Chong Liu & David J. Promel, 2025. "Pathwise analysis of log-optimal portfolios," Papers 2507.18232, arXiv.org.
    • Handle: RePEc:arx:papers:2507.18232
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    References listed on IDEAS

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    1. Thaleia Zariphopoulou, 1999. "Optimal investment and consumption models with non-linear stock dynamics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(2), pages 271-296, October.
    2. Alexander Schied & Leo Speiser & Iryna Voloshchenko, 2016. "Model-free portfolio theory and its functional master formula," Papers 1606.03325, arXiv.org, revised May 2018.
    3. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    4. Andrew L. Allan & Christa Cuchiero & Chong Liu & David J. Prömel, 2023. "Model‐free portfolio theory: A rough path approach," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 709-765, July.
    5. Goll, Thomas & Kallsen, Jan, 2000. "Optimal portfolios for logarithmic utility," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 31-48, September.
    6. Larsen, Kasper & Zitkovic, Gordan, 2007. "Stability of utility-maximization in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1642-1662, November.
    7. Andrew L. Allan & Chong Liu & David J. Prömel, 2024. "A càdlàg rough path foundation for robust finance," Finance and Stochastics, Springer, vol. 28(1), pages 215-257, January.
    8. Ariel Neufeld & Mario Sikic, 2016. "Robust Utility Maximization in Discrete-Time Markets with Friction," Papers 1610.09230, arXiv.org, revised May 2018.
    9. Ioannis Karatzas & Donghan Kim, 2020. "Trading strategies generated pathwise by functions of market weights," Finance and Stochastics, Springer, vol. 24(2), pages 423-463, April.
    10. L.C.G. Rogers, 2001. "The relaxed investor and parameter uncertainty," Finance and Stochastics, Springer, vol. 5(2), pages 131-154.
    11. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    12. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-161.
    13. Holger Kraft, 2005. "Optimal portfolios and Heston's stochastic volatility model: an explicit solution for power utility," Quantitative Finance, Taylor & Francis Journals, vol. 5(3), pages 303-313.
    14. Nicolas Perkowski & David J. Promel, 2013. "Pathwise stochastic integrals for model free finance," Papers 1311.6187, arXiv.org, revised Jun 2016.
    15. Paolo Guasoni & Scott Robertson, 2012. "Portfolios and risk premia for the long run," Papers 1203.1399, arXiv.org.
    16. Masaaki Fukasawa, 2014. "Efficient discretization of stochastic integrals," Finance and Stochastics, Springer, vol. 18(1), pages 175-208, January.
    17. Mathieu Rosenbaum & Peter Tankov, 2011. "Asymptotically optimal discretization of hedging strategies with jumps," Papers 1108.5940, arXiv.org, revised Apr 2014.
    18. Kim Weston, 2016. "Stability of utility maximization in nonequivalent markets," Finance and Stochastics, Springer, vol. 20(2), pages 511-541, April.
    19. Ralf Korn, 1997. "Optimal Portfolios:Stochastic Models for Optimal Investment and Risk Management in Continuous Time," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 3548, October.
    20. Emmanuel Temam & Emmanuel Gobet, 2001. "Discrete time hedging errors for options with irregular payoffs," Finance and Stochastics, Springer, vol. 5(3), pages 357-367.
    21. Huyên Pham & Xiaoli Wei & Chao Zhou, 2022. "Portfolio diversification and model uncertainty: A robust dynamic mean‐variance approach," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 349-404, January.
    22. Kasper Larsen & Gordan Zitkovic, 2007. "Stability of utility-maximization in incomplete markets," Papers 0706.0474, arXiv.org.
    23. Ariel Neufeld & Marcel Nutz, 2018. "Robust Utility Maximization With Lã‰Vy Processes," Mathematical Finance, Wiley Blackwell, vol. 28(1), pages 82-105, January.
    24. Oleksii Mostovyi & Mihai Sîrbu, 2019. "Sensitivity analysis of the utility maximisation problem with respect to model perturbations," Finance and Stochastics, Springer, vol. 23(3), pages 595-640, July.
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