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.
"Hybrid Atlas models." Ann. Appl. Probab. 21 (2) 609 - 644, April 2011. https://doi.org/10.1214/10-AAP706