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.Comment: Published in at http://dx.doi.org/10.1214/10-AAP706 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
We examine the behavior of $n$ Brownian particles diffusing on the real line
with bounded, measurable drift and bounded, piecewise continuous diffusion
coefficients that depend on the current configuration of particles. Sufficient
conditions are established for the absence and for the presence of triple
collisions among the particles. As an application to the Atlas model for equity
markets, we study a special construction of such systems of diffusing particles
using Brownian motions with reflection on polyhedral domains.Comment: Published in at http://dx.doi.org/10.1214/09-AAP641 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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