A Limit Theorem for Financial Markets with Inert Investors
Please always quote using this URN:urn:nbn:de:0296-matheon-857
- 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.
Author: | Erhan Bayraktar, Ulrich Horst, Ronnie Sircar |
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URN: | urn:nbn:de:0296-matheon-857 |
Referee: | Hans Föllmer |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2004/02/13 |
Release Date: | 2004/02/13 |
Institute: | Humboldt-Universität zu Berlin |
Technische Universität Berlin | |
Preprint Number: | 76 |