Atlas models of equity markets

Abstract

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.

Published at http://dx.doi.org/10.1214/105051605000000449 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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• The Euler scheme for stochastic differential equations with discontinuous drift coefficient: A numerical study of the convergence rate
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• Planar Diffusions with Rank-Based Characteristics: Transition Probabilities, Time Reversal, Maximality and Perturbed Tanaka equations
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• Large systems of diffusions interacting through their ranks
• Brownian motion with asymptotically normal reflection in unbounded domains: from transience to stability
• A combinatorial analysis of interacting diffusions
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• Reflected Brownian Motion in a wedge: sum-of-exponential absorption probability at the vertex and differential properties
• High moments of the SHE in the clustering regimes
• The Inert Drift Atlas Model
• Exponential ergodicity and convergence for generalized reflected Brownian motion
• Stratonovich representation of semimartingale rank processes
• Optimal Surviving Strategy for Drifted Brownian Motions with Absorption
• Reflected Brownian Motion in a Convex Polyhedral Cone: Tail Estimates for the Stationary Distribution
• A Rank-Based Approach to Zipf's Law
• Large Rank-Based Models with Common Noise
• A Stock Market Model Based on CAPM and Market Size
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• Reflected Backward Stochastic Differential Equation with Rank-based Data
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• A construction of infinite Brownian particle systems
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