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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

    as
    1. Ioannis Karatzas & Johannes Ruf, 2017. "Trading strategies generated by Lyapunov functions," Finance and Stochastics, Springer, vol. 21(3), pages 753-787, July.
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    9. Ting-Kam Leonard Wong, 2017. "On portfolios generated by optimal transport," Papers 1709.03169, arXiv.org, revised Sep 2017.
    10. 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.
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    13. 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..
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    15. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29, January.
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