Diversity and Arbitrage in a Regulatory Breakup Model

Winslow Strong and Jean-Pierre Fouque

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Abstract: In 1999 Robert Fernholz observed an inconsistency between the normative assumption of existence of an equivalent martingale measure (EMM) and the empirical reality of diversity in equity markets. We explore a method of imposing diversity on market models by a type of antitrust regulation that is compatible with EMMs. The regulatory procedure breaks up companies that become too large, while holding the total number of companies constant by imposing a simultaneous merge of other companies. The regulatory events are assumed to have no impact on portfolio values. As an example, regulation is imposed on a market model in which diversity is maintained via a log-pole in the drift of the largest company. The result is the removal of arbitrage opportunities from this market while maintaining the market's diversity.

Date: 2010-03, Revised 2010-12
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Published in Annals of Finance, Vol. 7, No. 3, 349-374, 2011

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