The Annals of Applied Probability

Hybrid Atlas models

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

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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

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

First available in Project Euclid: 22 March 2011

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Zentralblatt MATH identifier

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

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


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.

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