A Limit Theorem for Financial Markets with Inert Investors

Mathematics of Operations Research, 2006, Volume 31 (4), 789-810.

25 Pages Posted: 30 May 2016  

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Ulrich Horst

Humboldt University of Berlin

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering

Date Written: December 1, 2004

Abstract

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.

Keywords: Semi-Markov processes; fractional Brownian motion; functional central limit theorem; market microstructure; investor inertia.

Suggested Citation

Bayraktar, Erhan and Horst, Ulrich and Sircar, Ronnie, A Limit Theorem for Financial Markets with Inert Investors (December 1, 2004). Mathematics of Operations Research, 2006, Volume 31 (4), 789-810.. Available at SSRN: https://ssrn.com/abstract=2785859

Erhan Bayraktar (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Ulrich Horst

Humboldt University of Berlin ( email )

Unter den Linden 6
Berlin, Berlin 10099
Germany

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering ( email )

Princeton, NJ 08544
United States

Paper statistics

Downloads
15
Abstract Views
232