Journal of Applied Mathematics and Stochastic Analysis
Volume 2009 (2009), Article ID 215817, 16 pages
Research Article

On Modelling Long Term Stock Returns with Ergodic Diffusion Processes: Arbitrage and Arbitrage-Free Specifications

School of Actuarial Studies, Australian School of Business, University of New South Wales, NSW 2052, Australia

Received 13 March 2009; Accepted 29 July 2009

Academic Editor: Vo Anh

Copyright © 2009 Bernard Wong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We investigate the arbitrage-free property of stock price models where the local martingale component is based on an ergodic diffusion with a specified stationary distribution. These models are particularly useful for long horizon asset-liability management as they allow the modelling of long term stock returns with heavy tail ergodic diffusions, with tractable, time homogeneous dynamics, and which moreover admit a complete financial market, leading to unique pricing and hedging strategies. Unfortunately the standard specifications of these models in literature admit arbitrage opportunities. We investigate in detail the features of the existing model specifications which create these arbitrage opportunities and consequently construct a modification that is arbitrage free.