- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 401562, 9 pages
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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- S. Asmussen, “Risk theory in a Markovian environment,” Scandinavian Actuarial Journal, no. 2, pp. 69–100, 1989.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- C. W. Clenshaw and A. R. Curtis, “A method for numerical integration on an automatic computer,” Numerische Mathematik, vol. 2, pp. 197–205, 1960.