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

2011/08/01 by Tomoyuki Ichiba, Soumik Pal, Ichiba, Tomoyuki +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #60G07 #60K35 #91B26 #Complex Systems and Time Series Analysis #Economic theories and models #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1108.0384

openalex publication_date 2011/08/01 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We determine rates of convergence of rank-based interacting diffusions and\nsemimartingale reflecting Brownian motions to equilibrium. Convergence rate for\nthe total variation metric is derived using Lyapunov functions. Sharp\nfluctuations of additive functionals are obtained using Transportation\nCost-Information inequalities for Markov processes. We work out various\napplications to the rank-based abstract equity markets used in Stochastic\nPortfolio Theory. For example, we produce quantitative bounds, including\nconstants, for fluctuations of market weights and occupation times of various\nranks for individual coordinates. Another important application is the\ncomparison of performance between symmetric functionally generated portfolios\nand the market portfolio. This produces estimates of probabilities of "beating\nthe market".\n

Citations

• Concentration of measure for systems of Brownian particles interacting\n through their ranks
• Foundations of Modern Probability

Cited by

• Convergence and Wave Propagation for a System of Branching Rank-Based Interacting Brownian Particles

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