The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 26, Number 3 (2016), 1329-1361.
Diverse market models of competing Brownian particles with splits and mergers
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.
Ann. Appl. Probab., Volume 26, Number 3 (2016), 1329-1361.
Received: April 2014
Revised: February 2015
First available in Project Euclid: 14 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60J60: Diffusion processes [See also 58J65]
Secondary: 91B26: Market models (auctions, bargaining, bidding, selling, etc.)
Karatzas, Ioannis; Sarantsev, Andrey. Diverse market models of competing Brownian particles with splits and mergers. Ann. Appl. Probab. 26 (2016), no. 3, 1329--1361. doi:10.1214/15-AAP1118. https://projecteuclid.org/euclid.aoap/1465905005