{
  "id": "math/0703831",
  "version": "v1",
  "published": "2007-03-28T05:24:45.000Z",
  "updated": "2007-03-28T05:24:45.000Z",
  "title": "A Limit Theorem for Financial Markets with Inert Investors",
  "authors": [
    "Erhan Bayraktar",
    "Ulrich Horst",
    "Ronnie Sircar"
  ],
  "journal": "Mathematics of Operations Research, 2006, Volume 31 (4), 789-810",
  "categories": [
    "math.PR",
    "q-fin.ST"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-28T05:24:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F13",
      "60G15",
      "91B28"
    ],
    "keywords": [
      "inert investors",
      "financial markets",
      "fractional brownian motion",
      "functional central limit theorem",
      "investor inertia"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3831B"
    }
  }
}