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Convergence rates for rank-based models with applications to portfolio theory
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  • Published: 27 May 2012

Convergence rates for rank-based models with applications to portfolio theory

  • Tomoyuki Ichiba1,
  • Soumik Pal2 &
  • Mykhaylo Shkolnikov3 

Probability Theory and Related Fields volume 156, pages 415–448 (2013)Cite this article

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  • 26 Citations

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Abstract

We determine rates of convergence of rank-based interacting diffusions and semimartingale reflecting Brownian motions to equilibrium. Bounds on fluctuations of additive functionals are obtained using Transportation Cost-Information inequalities for Markov processes. We work out various applications to the rank-based abstract equity markets used in Stochastic Portfolio Theory. For example, we produce quantitative bounds, including constants, for fluctuations of market weights and occupation times of various ranks for individual coordinates. Another important application is the comparison of performance between symmetric functionally generated portfolios and the market portfolio. This produces estimates of probabilities of “beating the market”.

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Author information

Authors and Affiliations

  1. Department of Statistics and Applied Probability, University of California, Santa Barbara, CA, 93106, USA

    Tomoyuki Ichiba

  2. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    Soumik Pal

  3. Mathematical Sciences Research Institute, 17 Gauss Way, Berkeley, CA, 94720, USA

    Mykhaylo Shkolnikov

Authors
  1. Tomoyuki Ichiba
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  2. Soumik Pal
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  3. Mykhaylo Shkolnikov
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Corresponding author

Correspondence to Mykhaylo Shkolnikov.

Additional information

This research is partially supported by NSF grants DMS-1007563 and DMS-0806211.

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Cite this article

Ichiba, T., Pal, S. & Shkolnikov, M. Convergence rates for rank-based models with applications to portfolio theory. Probab. Theory Relat. Fields 156, 415–448 (2013). https://doi.org/10.1007/s00440-012-0432-5

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  • Received: 01 August 2011

  • Accepted: 25 April 2012

  • Published: 27 May 2012

  • Issue Date: June 2013

  • DOI: https://doi.org/10.1007/s00440-012-0432-5

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Keywords

  • Stochastic portfolio theory
  • Reflecting Brownian motion
  • Market weights

Mathematics Subject Classification

  • 60K35
  • 60G07
  • 91B26
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