DIVERSE MARKET MODELS OF COMPETING BROWNIAN PARTICLES WITH SPLITS AND MERGERS

• 成果类型: Article
• 署名作者: Karatzas, Ioannis; Sarantsev, Andrey
• 署名单位: Columbia University; University of Washington; University of Washington Seattle
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1118
• 发表日期: 2016
• 页码: 1329-1361
• 关键词: systems

摘要

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.