  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 models is based on systems of competing Brownian
particles: each company has a capitalization whose logarithm behaves as a
Brownian motion with drift and diffusion coefficients depending on its current
rank. We study such models with a fluctuating number of companies: If at some
moment the share of the total market capitalization of a company reaches a
fixed level, then the company is split into two parts of random size. Companies
are also allowed to merge, when an exponential clock rings. We find conditions
under which this system is nonexplosive (i.e., the number of companies remains
finite at all times) and diverse, yet does not admit arbitrage opportunities.
