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

DOI10.1007/s00440-012-0432-5zbMath1274.60291arXiv1108.0384OpenAlexW2056997795MaRDI QIDQ1955832

Soumik Pal, Tomoyuki Ichiba, Mykhaylo Shkolnikov

Publication date: 19 June 2013

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.0384

zbMATH Keywords

reflecting Brownian motionstochastic portfolio theorymarket weightsRank-based interacting diffusions

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) General theory of stochastic processes (60G07) Auctions, bargaining, bidding and selling, and other market models (91B26) Portfolio theory (91G10)

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Cites Work

• Unnamed Item
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• Large systems of diffusions interacting through their ranks
• Hybrid Atlas models
• A positive recurrent reflecting Brownian motion with divergent fluid path
• Competing particle systems evolving by interacting Lévy processes
• Archimedes' principle for Brownian liquid
• A combinatorial analysis of interacting diffusions
• Local times of ranked continuous semimartingales
• Propagation of chaos and Poincaré inequalities for a system of particles interacting through their CDF
• On collisions of Brownian particles
• A simple proof of the Poincaré inequality for a large class of probability measures
• Competing particle systems evolving by I.I.D. Increments
• Reflected Brownian motion with skew symmetric data in a polyhedral domain
• Reflected Brownian motion on an orthant
• Lyapunov functions for semimartingale reflecting Brownian motions
• The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator
• On the stability of the linear Skorokhod problem in an orthant
• Multidimensional reflected Brownian motions having exponential stationary distributions
• Uniqueness for diffusions with piecewise constant coefficients
• A boundary property of semimartingale reflecting Brownian motions
• On the structure of quasi-stationary competing particle systems
• Remarks on non-interacting conservative spin systems: the case of gamma distributions
• Weak convergence of the scaled median of independent Brownian motions
• Long time asymptotics for constrained diffusions in polyhedral domains
• One-dimensional Brownian particle systems with rank-dependent drifts
• A phase transition behavior for Brownian motions interacting through their ranks
• Transportation-information inequalities for Markov processes
• Atlas models of equity markets
• Characterization of invariant measures at the leading edge for competing particle systems
• Concentration of measure for Brownian particle systems interacting through their ranks
• A sufficient condition for the positive recurrence of a semimartingale reflecting Brownian motion in an orthant
• The adjoint process of a diffusion with reflecting barrier
• Eigenvalues and eigenvectors of some tridiagonal matrices with non-constant diagonal entries
• Stochastic Portfolio Theory: an Overview
• Foundations of Modern Probability
• Chernoff and Berry–Esséen inequalities for Markov processes
• The advantage of capitalism vs. socialism depends on the criterion
• Diffusion with “collisions” between particles