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.
Publié le : 2005-11-14
Classification:
Financial markets,
portfolios,
order statistics,
local times,
stochastic differential equations,
ergodic properties,
60H10,
91B28,
60J55
@article{1133965764,
author = {Banner, Adrian D. and Fernholz, Robert and Karatzas, Ioannis},
title = {Atlas models of equity markets},
journal = {Ann. Appl. Probab.},
volume = {15},
number = {1A},
year = {2005},
pages = { 2296-2330},
language = {en},
url = {http://dml.mathdoc.fr/item/1133965764}
}
Banner, Adrian D.; Fernholz, Robert; Karatzas, Ioannis. Atlas models of equity markets. Ann. Appl. Probab., Tome 15 (2005) no. 1A, pp. 2296-2330. http://gdmltest.u-ga.fr/item/1133965764/