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A second-order stock market model


  • Robert Fernholz
  • Tomoyuki Ichiba
  • Ioannis Karatzas


A first-order model for a stock market assigns to each stock a return parameter and a variance parameter that depend only on the rank of the stock. A second-order model assigns these parameters based on both the rank and the name of the stock. First- and second-order models exhibit stability properties that make them appropriate as a backdrop for the analysis of the idiosyncratic behavior of individual stocks. Methods for the estimation of the parameters of second-order models are developed in this paper.

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  • Robert Fernholz & Tomoyuki Ichiba & Ioannis Karatzas, 2013. "A second-order stock market model," Papers 1302.3870,
  • Handle: RePEc:arx:papers:1302.3870

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    References listed on IDEAS

    1. Tomoyuki Ichiba & Vassilios Papathanakos & Adrian Banner & Ioannis Karatzas & Robert Fernholz, 2009. "Hybrid Atlas models," Papers 0909.0065,, revised Apr 2011.
    2. Mitchel Y. Abolafia (ed.), 2005. "Markets," Books, Edward Elgar Publishing, number 2788.
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    Cited by:

    1. Sergey Sosnovskiy, 2015. "Market shape formation, statistical equilibrium and neutral evolution theory," Papers 1506.07163,
    2. Sergey Sosnovskiy, 2015. "On financial applications of the two-parameter Poisson-Dirichlet distribution," Papers 1501.01954,, revised Jul 2015.
    3. Benjamin Jourdain & Julien Reygner, 2013. "Capital distribution and portfolio performance in the mean-field Atlas model," Papers 1312.5660,, revised Aug 2014.
    4. Benjamin Jourdain & Julien Reygner, 2015. "Capital distribution and portfolio performance in the mean-field Atlas model," Post-Print hal-00921151, HAL.

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