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

Financial Applications of Bivariate Markov Processes

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.

Linked References

  1. H. Markowitz, “Portfolio selection,” Journal of Finance, vol. 7, pp. 77–91, 1952. View at Google Scholar
  2. H. M. Markowitz, Portfolio Selection: Efficient Diversification of Investments, Cowles Foundation for Research in Economics at Yale University, Monograph 16, John Wiley & Sons, New York, NY, USA, 1959.
  3. H. M. Markowitz, Mean-Variance Analysis in Portfolio Choice and Capital Markets, Basil Blackwell, Oxford, UK, 1987.
  4. J. Tobin, “Liquidity preference as behavior toward risk,” Review of Economic Studies, vol. 25, pp. 65–86, 1958. View at Google Scholar
  5. J. Tobin, “The theory of portfolio selection,” in The Theory of Interest Rates, F. H. Hahn and F. P. R. Brechling, Eds., Macmillan, London, UK, 1965. View at Google Scholar
  6. F. Lamantia, S. Ortobelli Lozza, and S. T. Rachev, “VaR, CVaR and time rules with elliptical and asymmetric stable distributed returns,” Investment Management and Financial Innovations, vol. 3, no. 4, pp. 19–39, 2006. View at Google Scholar
  7. J. Longestaey and P. Zangari, Riskmetrics-Technical Document, J.P. Morgan, New York, NY, USA, 4th edition, 1996.
  8. F. Black and M. Scholes, “The pricing of options and corporate liabilities,” Journal of Political Economy, vol. 81, pp. 637–654, 1973. View at Google Scholar
  9. S. Rachev and S. Mittnik, Stable Paretian Models in Finance, John Wiley & Sons, Chichester, UK, 2000.
  10. J. Duan, E. Dudley, G. Gauthier, and J. Simonato, “Pricing discretely monitored barrier options by a Markov chain,” Journal of Derivatives, vol. 10, pp. 9–23, 2003. View at Google Scholar
  11. E. Angelelli and S. Ortobelli Lozza, “American and European Portfolio Selection Strategies: The Markovian Approach,” in Financial Hedging, P. N. Catlere, Ed., chapter 5, pp. 119–152, Nova Science Publishers, 2009. View at Google Scholar
  12. J.-C. Duan and J.-G. Simonato, “American option pricing under GARCH by a Markov chain approximation,” Journal of Economic Dynamics & Control, vol. 25, no. 11, pp. 1689–1718, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. S. O. Lozza and A. Staino, “Exotic options with Lévy processes: the Markovian approach,” Investment Management and Financial Innovations, vol. 8, no. 1, pp. 140–156, 2011. View at Google Scholar
  14. G. D'Amico, “Statistical inference for Markov chain European option: estimating the price, the bare risk and the theta by historical distributions of Markov chain,” Journal of Statistics & Management Systems, vol. 9, no. 3, pp. 737–754, 2006. View at Google Scholar · View at Zentralblatt MATH
  15. Y. Aït-Sahalia and A. W. Lo, “Nonparametric estimation of state-price densities implicit in financial asset prices,” Journal of Finance, vol. 53, no. 2, pp. 499–547, 1998. View at Google Scholar
  16. Y. Aít-Sahalia, “Nonparametric pricing of interest rate derivative securities,” Econometrica, vol. 64, no. 3, pp. 527–560, 1996. View at Google Scholar
  17. J. M. Hutchinson, A. W. Lo, and T. Poggio, “A non parametric approach to the pricing and hedging of derivative securities via learning networks,” Journal of Finance, vol. 49, pp. 851–889, 1994. View at Google Scholar
  18. M. Stutzer, “A simple nonparametric approach to derivative security valuation,” Journal of Finance, vol. 51, no. 5, pp. 1633–1652, 1996. View at Google Scholar
  19. S. O. Lozza and F. Pellerey, “Market stochastic bounds with elliptical distributions,” Journal of Concrete and Applicable Mathematics, vol. 6, no. 3, pp. 293–314, 2008. View at Google Scholar · View at Zentralblatt MATH
  20. S. Ortobelli Lozza, D. Toninelli, and E. Angelelli, “Set-portfolio selection with the use of market stochastic bounds,” Tech. Rep., University of Bergamo, 2010. View at Google Scholar
  21. W. F. Sharpe, “The Sharpe ratio,” Journal of Portfolio Management, pp. 45–58, 1994. View at Google Scholar
  22. F. X. Diebold, A. Hickman, A. Inoue, and T. Schuermann, “Converting 1-day volatility to h-day volatility: scaling by root-h is worse than you think,” Working Paper, Wharton Financial Institutions Center, pp. 97-34, 1998.
  23. F. X. Diebold, A. Hickman, A. Inoue, and T. Schuermann, “Scale models,” Risk, vol. 11, pp. 104–107, 1998. View at Google Scholar
  24. I. Kondor, S. Pafka, and G. Nagy, “Noise sensitivity of portfolio selection under various risk measures,” Journal of Banking and Finance, vol. 31, no. 5, pp. 1545–1573, 2007. View at Publisher · View at Google Scholar
  25. P. F. Christoffersen, “Evaluating interval forecasts,” International Economic Review, vol. 39, no. 4, pp. 841–862, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  26. G. Iaquinta and S. Ortobelli Lozza, “Markov chain applications to non parametric option pricing theory,” International Journal of Computer Science & Network Security, vol. 8, no. 6, pp. 199–208, 2008. View at Google Scholar