Atlas models of equity markets

By Adrian Banner, Robert Fernholz, Ioannis Karatzas. 2005

173 citations recorded by the source corpus.

Atlas-type models are constant-parameter models of uncorrelated stocks for equity markets with a stable capital distribution, in which the growth rates and variances depend on rank. The simplest such model assigns the same, constant variance to all stocks; zero rate of growth to all stocks but the smallest; and positive growth rate to the smallest, the Atlas stock. In this paper we study the basic properties of this class of models, as well as the behavior of various portfolios in their midst. Of particular interest are portfolios that do not contain the Atlas stock.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/782fb400b8c9a52c88f8ce6edc71d9308465bf2c

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Citations in the corpus

On collisions of Brownian particles (2008, background): “introduced by Fernholz (5) and studied by Banner, Fernholz & Karatzas (1).”
Strong solutions of stochastic equations with rank-based coefficients (2011, background): “It was observed in [1] that Proposition 3 permits the identification of the process of ordered particles (X(1), .”
Local times of ranked continuous semimartingales (2008, unknown): “Fernholz’s monograph [2], and the Atlas and first-order models studied in [2] and [1].”
Systems of Brownian particles with asymmetric collisions (2012, methodology): “Lévy theorem (see Section 3 in [2] for a very similar derivation).”
HYBRID ATLAS MODELS (2009, methodology): “In this paper we generalize the first-order models by introducing name-based effects of companies, in addition to the purely rank-based effects of the simpler models studied in [3].”
Convergence rates for rank-based models with applications to portfolio theory (2011, methodology): “This is a departure from the usual Black-Scholes models that cesses represented by continuous semimartingales (see, e.g., Duffie (1992) or Karatzas and Shreve (1998)).”
ONE-DIMENSIONAL BROWNIAN PARTICLE SYSTEMS WITH RANK DEPENDENT DRIFTS (2007, background): “The general rank-dependent interacting Brownian models, whose drifts and volatilities depend on time-varying ranks, have been considered by Banner, Fernholz and Karatzas in [3], with whom our work in this paper bears close resemblance.”