The Annals of Applied Probability

Hybrid Atlas models

Tomoyuki Ichiba, Vassilios Papathanakos, Adrian Banner, Ioannis Karatzas, and Robert Fernholz

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Abstract

We study Atlas-type models of equity markets with local characteristics that depend on both name and rank, and in ways that induce a stable capital distribution. Ergodic properties and rankings of processes are examined with reference to the theory of reflected Brownian motions in polyhedral domains. In the context of such models we discuss properties of various investment strategies, including the so-called growth-optimal and universal portfolios.

Article information

Source
Ann. Appl. Probab. Volume 21, Number 2 (2011), 609-644.

Dates
First available in Project Euclid: 22 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1300800983

Digital Object Identifier
doi:10.1214/10-AAP706

Mathematical Reviews number (MathSciNet)
MR2807968

Zentralblatt MATH identifier
1230.60046

Subjects
Primary: 60G44: Martingales with continuous parameter 91B28
Secondary: 70F10: $n$-body problems

Keywords
Diffusion processes interacting through their ranks reflected Brownian motions in polyhedral domains invariant measure of diffusion growth-optimal and universal portfolios local times of Bessel processes

Citation

Ichiba, Tomoyuki; Papathanakos, Vassilios; Banner, Adrian; Karatzas, Ioannis; Fernholz, Robert. Hybrid Atlas models. Ann. Appl. Probab. 21 (2011), no. 2, 609--644. doi:10.1214/10-AAP706. https://projecteuclid.org/euclid.aoap/1300800983


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