A limit theorem for financial markets with inert investors

• 成果类型: Article
• 署名作者: Bayraktar, Erhan; Horst, Ulrich; Sircar, Ronnie
• 署名单位: University of Michigan System; University of Michigan; University of British Columbia; Princeton University; Princeton University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1060.0202
• 发表日期: 2006
• 页码: 789-810
• 关键词: brownian-motion; arbitrage; BEHAVIOR; internet; returns; chaos

摘要

We study the effect of investor inertia on stock price fluctuations with a market microstructure model comprising many small investors who are inactive most of the time. It turns out that semi-Markov processes are tailor made for modelling inert investors. With a suitable scaling, we show that when the price is driven by the market imbalance, the log price process is approximated by a process with long-range dependence and non-Gaussian returns distributions, driven by a fractional Brownian motion. Consequently, investor inertia may lead to arbitrage opportunities for sophisticated market participants. The mathematical contributions are a functional central limit theorem for stationary semi-Markov processes and approximation results for stochastic integrals of continuous semimartingales with respect to fractional Brownian motion.