On the Expected Discounted Penalty Function for a Markov Regime-Switching Insurance Risk Model with Stochastic Premium Income
We consider a Markovian regime-switching risk model (also called the Markov-modulated risk model) with stochastic premium income, in which the premium income and the claim occurrence are driven by the Markovian regime-switching process. The purpose of this paper is to study the integral equations sa...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/320146 |
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| _version_ | 1832560461224083456 |
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| author | Wenguang Yu |
| author_facet | Wenguang Yu |
| author_sort | Wenguang Yu |
| collection | DOAJ |
| description | We consider a Markovian regime-switching risk model (also called the Markov-modulated risk model) with stochastic premium income, in which the premium income and the claim occurrence are driven by the Markovian regime-switching process. The purpose of this paper is to study the integral equations satisfied by the expected discounted penalty function. In particular, the discount interest force process is also regulated by the Markovian regime-switching process. Applications of the integral equations are given to be the Laplace transform of the time of ruin, the deficit at ruin, and the surplus immediately before ruin occurs. For exponential distribution, the explicit expressions for these quantities are obtained. Finally, a numerical example is also given to illustrate the effect of the related parameters
on these quantities. |
| format | Article |
| id | doaj-art-03bcac2267154effbbdfe58135c1ff6d |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-03bcac2267154effbbdfe58135c1ff6d2025-02-03T01:27:31ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/320146320146On the Expected Discounted Penalty Function for a Markov Regime-Switching Insurance Risk Model with Stochastic Premium IncomeWenguang Yu0School of Mathematics, Shandong University, Jinan 250100, ChinaWe consider a Markovian regime-switching risk model (also called the Markov-modulated risk model) with stochastic premium income, in which the premium income and the claim occurrence are driven by the Markovian regime-switching process. The purpose of this paper is to study the integral equations satisfied by the expected discounted penalty function. In particular, the discount interest force process is also regulated by the Markovian regime-switching process. Applications of the integral equations are given to be the Laplace transform of the time of ruin, the deficit at ruin, and the surplus immediately before ruin occurs. For exponential distribution, the explicit expressions for these quantities are obtained. Finally, a numerical example is also given to illustrate the effect of the related parameters on these quantities.http://dx.doi.org/10.1155/2013/320146 |
| spellingShingle | Wenguang Yu On the Expected Discounted Penalty Function for a Markov Regime-Switching Insurance Risk Model with Stochastic Premium Income Discrete Dynamics in Nature and Society |
| title | On the Expected Discounted Penalty Function for a Markov Regime-Switching Insurance Risk Model with Stochastic Premium Income |
| title_full | On the Expected Discounted Penalty Function for a Markov Regime-Switching Insurance Risk Model with Stochastic Premium Income |
| title_fullStr | On the Expected Discounted Penalty Function for a Markov Regime-Switching Insurance Risk Model with Stochastic Premium Income |
| title_full_unstemmed | On the Expected Discounted Penalty Function for a Markov Regime-Switching Insurance Risk Model with Stochastic Premium Income |
| title_short | On the Expected Discounted Penalty Function for a Markov Regime-Switching Insurance Risk Model with Stochastic Premium Income |
| title_sort | on the expected discounted penalty function for a markov regime switching insurance risk model with stochastic premium income |
| url | http://dx.doi.org/10.1155/2013/320146 |
| work_keys_str_mv | AT wenguangyu ontheexpecteddiscountedpenaltyfunctionforamarkovregimeswitchinginsuranceriskmodelwithstochasticpremiumincome |