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math.PR2018
Large Rank-Based Models with Common Noise
Praveen Kolli, Andrey Sarantsev
For large systems of Brownian particles interacting through their ranks introduced in (Banner, Fernholz, Karatzas, 2005), the empirical cumulative distribution function satisfies a…
math.PR2016
A Note on Jump Atlas Models
Clayton Barnes, Andrey Sarantsev
The market weight of a stock is its capitalization (cap) divided by the total market cap. Rank these weights from top to bottom. The capital distribution curve is a plot of weights…
math.PR2014★ 11 cited
Diverse market models of competing Brownian particles with splits and mergers
Ioannis Karatzas, Andrey Sarantsev
We study models of regulatory breakup, in the spirit of Strong and Fouque [Ann. Finance 7 (2011) 349-374] but with a fluctuating number of companies. An important class of market m…