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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, 2023. "Quantifying dimensional change in stochastic portfolio theory," Papers 2303.00858, arXiv.org, revised Apr 2023.
    • Handle: RePEc:arx:papers:2303.00858
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    References listed on IDEAS

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    1. David Itkin & Martin Larsson, 2021. "Open Markets and Hybrid Jacobi Processes," Papers 2110.14046, arXiv.org, revised Mar 2024.
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    11. Erhan Bayraktar & Donghan Kim & Abhishek Tilva, 2022. "Arbitrage theory in a market of stochastic dimension," Papers 2212.04623, arXiv.org, revised Jun 2023.
    12. Ruf, Johannes & Xie, Kangjianan, 2019. "Generalised Lyapunov functions and functionally generated trading strategies," LSE Research Online Documents on Economics 102424, London School of Economics and Political Science, LSE Library.
    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..
    14. Donghan Kim, 2022. "Market-to-book Ratio in Stochastic Portfolio Theory," Papers 2206.03742, arXiv.org.
    15. 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.
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