Table of Contents
International Journal of Stochastic Analysis
Volume 2011, Article ID 501360, 11 pages
http://dx.doi.org/10.1155/2011/501360
Research Article

First Passage Time Moments of Jump-Diffusions with Markovian Switching

Department of Mathematical Sciences, Central South University, Changsha, Hunan, China

Received 5 December 2010; Accepted 24 January 2011

Academic Editor: Enzo Orsingher

Copyright © 2011 Jun Peng and Zaiming Liu. 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. D. A. Darling and A. J. F. Siegert, “A systematic approach to a class of problems in the theory of noise and other random phenomena—part I,” IRE Transactions on Information Theory, vol. 3, pp. 32–37, 1957. View at Publisher · View at Google Scholar
  2. W. Schwert, “Why does stock market volatility change over time ?” Journal of Finance, vol. 44, pp. 1115–1153, 1989. View at Publisher · View at Google Scholar
  3. J. Lewellen, “Predicting returns with financial ratios,” Journal of Financial Economics, vol. 74, no. 2, pp. 209–235, 2004. View at Publisher · View at Google Scholar
  4. H. C. Tuckwell, “On the first-exit time problem for temporally homogeneous Markov processes,” Journal of Applied Probability, vol. 13, no. 1, pp. 39–48, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. P. Patie and C. Winter, “First exit time probability for multidimensional diffusions: a PDE-based approach,” Journal of Computational and Applied Mathematics, vol. 222, no. 1, pp. 42–53, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. S. G. Kou and H. Wang, “First passage times of a jump diffusion process,” Advances in Applied Probability, vol. 35, no. 2, pp. 504–531, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. R. Z. Khasminskii, C. Zhu, and G. Yin, “Stability of regime-switching diffusions,” Stochastic Processes and Their Applications, vol. 117, no. 8, pp. 1037–1051, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. F. Xi, “On the stability of jump-diffusions with Markovian switching,” Journal of Mathematical Analysis and Applications, vol. 341, no. 1, pp. 588–600, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. I. I. Gihman and A. V. Skorohod, Stochastic Differential Equations, Springer, New York, NY, USA, 1972.
  10. A. Di Crescenzo, E. Di Nardo, and L. M. Ricciardi, “Simulation of first-passage times for alternating Brownian motions,” Methodology and Computing in Applied Probability, vol. 7, no. 2, pp. 161–181, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. G. B. Di Masi, Y. M. Kabanov, and V. I. Runggaldier, “Mean-square hedging of options on a stock with Markov volatilities,” Theory of Probability and Its Applications, vol. 39, pp. 172–182, 1995. View at Google Scholar
  12. N. Ratanov, “Option pricing model based on a Markov-modulated diffusion with jumps,” Brazilian Journal of Probability and Statistics, vol. 24, no. 2, pp. 413–431, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. R. Rishel, “Whether to sell or hold a stock,” Communications in Information and Systems, vol. 6, no. 3, pp. 193–202, 2006. View at Google Scholar · View at Zentralblatt MATH