Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 347604, 15 pages
http://dx.doi.org/10.1155/2011/347604
Research Article

Financial Applications of Bivariate Markov Processes

Sergio Ortobelli Lozza,1 Enrico Angelelli,2 and Annamaria Bianchi1

1Department MSIA, University of Bergamo, Via dei Caniana 2, 24127 Bergamo, Italy
2Department of Quantitative Methods, University of Brescia, Contrada Santa Chiara 50, 25122 Brescia, Italy

Received 14 April 2011; Accepted 4 September 2011

Academic Editor: Jitao Sun

Copyright © 2011 Sergio Ortobelli Lozza et al. 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.

Abstract

This paper describes a methodology to approximate a bivariate Markov process by means of a proper Markov chain and presents possible financial applications in portfolio theory, option pricing and risk management. In particular, we first show how to model the joint distribution between market stochastic bounds and future wealth and propose an application to large-scale portfolio problems. Secondly, we examine an application to VaR estimation. Finally, we propose a methodology to price Asian options using a bivariate Markov process.