Diversity and no arbitrage
Portfolio Management
2014-08-26 v2 Probability
Abstract
A stock market is called diverse if no stock can dominate the market in terms of relative capitalization. On one hand, this natural property leads to arbitrage in diffusion models under mild assumptions. On the other hand, it is also easy to construct diffusion models which are both diverse and free of arbitrage. Can one tell whether an observed diverse market admits arbitrage? In the present paper we argue that this may well be impossible by proving that the known examples of diverse markets in the literature (which do admit arbitrage) can be approximated uniformly (on the logarithmic scale) by models which are both diverse and arbitrage-free.
Cite
@article{arxiv.1301.4173,
title = {Diversity and no arbitrage},
author = {Attila Herczegh and Vilmos Prokaj and Miklós Rásonyi},
journal= {arXiv preprint arXiv:1301.4173},
year = {2014}
}
Comments
14 pages, final version