On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes
We focus on the expected discounted penalty function of a compound Poisson risk model with random incomes and potentially delayed claims. It is assumed that each main claim will produce a byclaim with a certain probability and the occurrence of the byclaim may be delayed depending on associated main...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/717269 |
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| _version_ | 1832551861904736256 |
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| author | Huiming Zhu Ya Huang Xiangqun Yang Jieming Zhou |
| author_facet | Huiming Zhu Ya Huang Xiangqun Yang Jieming Zhou |
| author_sort | Huiming Zhu |
| collection | DOAJ |
| description | We focus on the expected discounted penalty function of a compound Poisson risk model with random incomes and potentially delayed claims. It is assumed that each main claim will produce a byclaim with a certain probability and the occurrence of the byclaim may be delayed depending on associated main claim amount. In addition, the premium number process is assumed as a Poisson process. We derive the integral equation satisfied by the expected discounted penalty function. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the expected discounted penalty function is derived. Finally, for the exponential claim sizes, we present the explicit formula for the expected discounted penalty function. |
| format | Article |
| id | doaj-art-1f892215cdf544fda1bc59cabb6156ff |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-1f892215cdf544fda1bc59cabb6156ff2025-02-03T06:00:19ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/717269717269On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random IncomesHuiming Zhu0Ya Huang1Xiangqun Yang2Jieming Zhou3College of Business Administration, Hunan University, Changsha 410082, ChinaCollege of Business Administration, Hunan University, Changsha 410082, ChinaCollege of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, ChinaSchool of Mathematical Sciences, Nankai University, Tianjin 300071, ChinaWe focus on the expected discounted penalty function of a compound Poisson risk model with random incomes and potentially delayed claims. It is assumed that each main claim will produce a byclaim with a certain probability and the occurrence of the byclaim may be delayed depending on associated main claim amount. In addition, the premium number process is assumed as a Poisson process. We derive the integral equation satisfied by the expected discounted penalty function. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the expected discounted penalty function is derived. Finally, for the exponential claim sizes, we present the explicit formula for the expected discounted penalty function.http://dx.doi.org/10.1155/2014/717269 |
| spellingShingle | Huiming Zhu Ya Huang Xiangqun Yang Jieming Zhou On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes Journal of Applied Mathematics |
| title | On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes |
| title_full | On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes |
| title_fullStr | On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes |
| title_full_unstemmed | On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes |
| title_short | On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes |
| title_sort | on the expected discounted penalty function for the classical risk model with potentially delayed claims and random incomes |
| url | http://dx.doi.org/10.1155/2014/717269 |
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