Numerical Method for a Markov-Modulated Risk Model with Two-Sided Jumps
This paper considers a perturbed Markov-modulated risk model with two-sided jumps, where both the upward and downward jumps follow arbitrary distribution. We first derive a system of differential equations for the Gerber-Shiu function. Furthermore, a numerical result is given based on Chebyshev poly...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/401562 |
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| _version_ | 1832568218764443648 |
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| author | Hua Dong Xianghua Zhao |
| author_facet | Hua Dong Xianghua Zhao |
| author_sort | Hua Dong |
| collection | DOAJ |
| description | This paper considers a perturbed Markov-modulated risk model with two-sided jumps, where both the upward and downward jumps follow arbitrary distribution. We first derive a system of differential equations for the Gerber-Shiu function. Furthermore, a numerical result is given based on Chebyshev polynomial approximation. Finally, an example is provided to illustrate the method. |
| format | Article |
| id | doaj-art-6e1b93c43fb542bda9aa8600f3962f2f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-6e1b93c43fb542bda9aa8600f3962f2f2025-02-03T00:59:30ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/401562401562Numerical Method for a Markov-Modulated Risk Model with Two-Sided JumpsHua Dong0Xianghua Zhao1School of Mathematical Sciences, Qufu Normal University, Qufu 273165, ChinaSchool of Mathematical Sciences, Qufu Normal University, Qufu 273165, ChinaThis paper considers a perturbed Markov-modulated risk model with two-sided jumps, where both the upward and downward jumps follow arbitrary distribution. We first derive a system of differential equations for the Gerber-Shiu function. Furthermore, a numerical result is given based on Chebyshev polynomial approximation. Finally, an example is provided to illustrate the method.http://dx.doi.org/10.1155/2012/401562 |
| spellingShingle | Hua Dong Xianghua Zhao Numerical Method for a Markov-Modulated Risk Model with Two-Sided Jumps Abstract and Applied Analysis |
| title | Numerical Method for a Markov-Modulated Risk Model with Two-Sided Jumps |
| title_full | Numerical Method for a Markov-Modulated Risk Model with Two-Sided Jumps |
| title_fullStr | Numerical Method for a Markov-Modulated Risk Model with Two-Sided Jumps |
| title_full_unstemmed | Numerical Method for a Markov-Modulated Risk Model with Two-Sided Jumps |
| title_short | Numerical Method for a Markov-Modulated Risk Model with Two-Sided Jumps |
| title_sort | numerical method for a markov modulated risk model with two sided jumps |
| url | http://dx.doi.org/10.1155/2012/401562 |
| work_keys_str_mv | AT huadong numericalmethodforamarkovmodulatedriskmodelwithtwosidedjumps AT xianghuazhao numericalmethodforamarkovmodulatedriskmodelwithtwosidedjumps |