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Quantifying dimensional change in stochastic portfolio theory

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Listed:
  • Erhan Bayraktar
  • Donghan Kim
  • Abhishek Tilva

Abstract

In this paper, we develop the theory of functional generation of portfolios in an equity market with changing dimension. By introducing dimensional jumps in the market, as well as jumps in stock capitalization between the dimensional jumps, we construct different types of self‐financing stock portfolios (additive, multiplicative, and rank‐based) in a very general setting. Our study explains how a dimensional change caused by a listing or delisting event of a stock, and unexpected shocks in the market, affect portfolio return. We also provide empirical analyses of some classical portfolios, quantifying the impact of dimensional change in portfolio performance relative to the market.

Suggested Citation

  • Erhan Bayraktar & Donghan Kim & Abhishek Tilva, 2024. "Quantifying dimensional change in stochastic portfolio theory," Mathematical Finance, Wiley Blackwell, vol. 34(3), pages 977-1021, July.
    • Handle: RePEc:bla:mathfi:v:34:y:2024:i:3:p:977-1021
    DOI: 10.1111/mafi.12425
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    References listed on IDEAS

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    1. Martin Herdegen, 2017. "No-Arbitrage In A Numéraire-Independent Modeling Framework," Mathematical Finance, Wiley Blackwell, vol. 27(2), pages 568-603, April.
    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. Ruf, Johannes & Xie, Kangjianan, 2020. "Impact of proportional transaction costs on systematically generated portfolios," LSE Research Online Documents on Economics 104696, London School of Economics and Political Science, LSE Library.
    4. Karatzas, Ioannis & Ruf, Johannes, 2017. "Trading strategies generated by Lyapunov functions," LSE Research Online Documents on Economics 69177, London School of Economics and Political Science, LSE Library.
    5. Erhan Bayraktar & Donghan Kim & Abhishek Tilva, 2024. "Arbitrage theory in a market of stochastic dimension," Mathematical Finance, Wiley Blackwell, vol. 34(3), pages 847-895, July.
    6. Patrick Mijatovic, 2021. "Beating the Market with Generalized Generating Portfolios," Papers 2101.07084, arXiv.org.
    7. 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.
    8. Johannes Ruf & Kangjianan Xie, 2019. "Generalised Lyapunov Functions and Functionally Generated Trading Strategies," Applied Mathematical Finance, Taylor & Francis Journals, vol. 26(4), pages 293-327, July.
    9. Ioannis Karatzas & Johannes Ruf, 2017. "Trading strategies generated by Lyapunov functions," Finance and Stochastics, Springer, vol. 21(3), pages 753-787, July.
    10. David Itkin & Martin Larsson, 2021. "Open Markets and Hybrid Jacobi Processes," Papers 2110.14046, arXiv.org, revised Mar 2024.
    11. Ting-Kam Wong, 2015. "Optimization of relative arbitrage," Annals of Finance, Springer, vol. 11(3), pages 345-382, November.
    12. Winslow Strong, 2014. "Fundamental theorems of asset pricing for piecewise semimartingales of stochastic dimension," Finance and Stochastics, Springer, vol. 18(3), pages 487-514, July.
    13. Ting-Kam Leonard Wong, 2017. "On portfolios generated by optimal transport," Papers 1709.03169, arXiv.org, revised Sep 2017.
    14. repec:ehl:lserod:102424 is not listed on IDEAS
    15. Robert Fernholz, 1999. "Portfolio Generating Functions," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 15, pages 344-367, World Scientific Publishing Co. Pte. Ltd..
    16. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29, January.
    17. Donghan Kim, 2022. "Market-to-book Ratio in Stochastic Portfolio Theory," Papers 2206.03742, arXiv.org.
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    Cited by:

    1. Steven Campbell & Qien Song & Ting-Kam Leonard Wong, 2024. "Macroscopic properties of equity markets: stylized facts and portfolio performance," Papers 2409.10859, arXiv.org, revised Oct 2024.

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