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

• 成果类型: Article
• 署名作者: Ichiba, Tomoyuki; Pal, Soumik; Shkolnikov, Mykhaylo
• 署名单位: University of California System; University of California Santa Barbara; University of Washington; University of Washington Seattle
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-012-0432-5
• 发表日期: 2013
• 页码: 415-448
• 关键词: reflecting brownian-motion; particle-systems; inequalities

摘要

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.