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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 401562, 9 pages
doi:10.1155/2012/401562
Research Article
Numerical Method for a Markov-Modulated Risk Model with Two-Sided Jumps
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
Received 24 August 2012; Accepted 30 October 2012
Academic Editor: Xinguang Zhang
Copyright © 2012 Hua Dong and Xianghua Zhao. 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
- R. J. Boucherie, O. J. Boxma, and K. Sigman, “A note on negative customers, workload, and risk processes,” Probability in the Engineering and Informational Sciences, vol. 11, no. 3, pp. 305–311, 1997. View at Publisher · View at Google Scholar
- 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
- X. Xing, W. Zhang, and Y. Jiang, “On the time to ruin and the deficit at ruin in a risk model with double-sided jumps,” Statistics & Probability Letters, vol. 78, no. 16, pp. 2692–2699, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- Z. Zhang, H. Yang, and S. Li, “The perturbed compound Poisson risk model with two-sided jumps,” Journal of Computational and Applied Mathematics, vol. 233, no. 8, pp. 1773–1784, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- Y. Chi, “Analysis of the expected discounted penalty function for a general jump-diffusion risk model and applications in finance,” Insurance: Mathematics & Economics, vol. 46, no. 2, pp. 385–396, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- M. Jacobsen, “The time to ruin for a class of Markov additive risk process with two-sided jumps,” Advances in Applied Probability, vol. 37, no. 4, pp. 963–992, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- S. Asmussen, “Risk theory in a Markovian environment,” Scandinavian Actuarial Journal, no. 2, pp. 69–100, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J. Zhu and H. Yang, “Ruin theory for a Markov regime-switching model under a threshold dividend strategy,” Insurance: Mathematics & Economics, vol. 42, no. 1, pp. 311–318, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J. Zhu and H. Yang, “On differentiability of ruin functions under Markov-modulated models,” Stochastic Processes and Their Applications, vol. 119, no. 5, pp. 1673–1695, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- A. C. Y. Ng and H. Yang, “On the joint distribution of surplus before and after ruin under a Markovian regime switching model,” Stochastic Processes and Their Applications, vol. 116, no. 2, pp. 244–266, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- S. Li and Y. Lu, “The decompositions of the discounted penalty functions and dividends-penalty identity in a Markov-modulated risk model,” ASTIN Bulletin, vol. 38, no. 1, pp. 53–71, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- Y. Lu and C. C. L. Tsai, “The expected discounted penalty at ruin for a Markov-modulated risk process perturbed by diffusion,” North American Actuarial Journal, vol. 11, no. 2, pp. 136–149, 2007.
- A. Akyüz-Dascioglu, “A Chebyshev polynomial approach for linear Fredholm-Volterra integro-differential equations in the most general form,” Applied Mathematics and Computation, vol. 181, no. 1, pp. 103–112, 2007. View at Publisher · View at Google Scholar
- P. Diko and M. Usábel, “A numerical method for the expected penalty-reward function in a Markov-modulated jump-diffusion process,” Insurance: Mathematics & Economics, vol. 49, no. 1, pp. 126–131, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- M. A. Fariborzi Araghi and S. S. Behzadi, “Numerical solution of nonlinear Volterra-Fredholm integro-differential equations using homotopy analysis method,” Journal of Applied Mathematics and Computing, vol. 37, no. 1-2, pp. 1–12, 2011. View at Publisher · View at Google Scholar
- C. W. Clenshaw and A. R. Curtis, “A method for numerical integration on an automatic computer,” Numerische Mathematik, vol. 2, pp. 197–205, 1960. View at Publisher · View at Google Scholar · View at Zentralblatt MATH