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

Tomoyuki Ichiba, Soumik Pal, Mykhaylo Shkolnikov

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


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".

Original languageEnglish (US)
Pages (from-to)415-448
Number of pages34
JournalProbability Theory and Related Fields
Issue number1-2
StatePublished - Jun 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Market weights
  • Reflecting Brownian motion
  • Stochastic portfolio theory


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