On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model
In this paper, we assume that the reserve level of an insurance company can only be observed at discrete time points, then a new risk model is proposed by introducing a periodic capital injection strategy and a barrier dividend strategy into the classical risk model. We derive the equations and the...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/4/511 |
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| author | Wenguang Yu Peng Guo Qi Wang Guofeng Guan Qing Yang Yujuan Huang Xinliang Yu Boyi Jin Chaoran Cui |
| author_facet | Wenguang Yu Peng Guo Qi Wang Guofeng Guan Qing Yang Yujuan Huang Xinliang Yu Boyi Jin Chaoran Cui |
| author_sort | Wenguang Yu |
| collection | DOAJ |
| description | In this paper, we assume that the reserve level of an insurance company can only be observed at discrete time points, then a new risk model is proposed by introducing a periodic capital injection strategy and a barrier dividend strategy into the classical risk model. We derive the equations and the boundary conditions satisfied by the Gerber-Shiu function, the expected discounted capital injection function and the expected discounted dividend function by assuming that the observation interval and claim amount are exponentially distributed, respectively. Numerical examples are also given to further analyze the influence of relevant parameters on the actuarial function of the risk model. |
| first_indexed | 2024-03-10T20:43:30Z |
| format | Article |
| id | doaj.art-fea5b1d4302b49bab8ce7da10dfb8c6a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T20:43:30Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-fea5b1d4302b49bab8ce7da10dfb8c6a2023-11-19T20:32:54ZengMDPI AGMathematics2227-73902020-04-018451110.3390/math8040511On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk ModelWenguang Yu0Peng Guo1Qi Wang2Guofeng Guan3Qing Yang4Yujuan Huang5Xinliang Yu6Boyi Jin7Chaoran Cui8School of Insurance, Shandong University of Finance and Economics, Jinan 250014, ChinaCollege of Mathematics and Statistics, Chongqing University, Chongqing 401331, ChinaSchool of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, ChinaSchool of Insurance, Shandong University of Finance and Economics, Jinan 250014, ChinaSchool of Insurance, Shandong University of Finance and Economics, Jinan 250014, ChinaSchool of Science, Shandong Jiaotong University, Jinan 250357, ChinaSchool of Insurance, Shandong University of Finance and Economics, Jinan 250014, ChinaSchool of Insurance, Shandong University of Finance and Economics, Jinan 250014, ChinaSchool of Computer Science & Technology, Shandong University of Finance and Economics, Jinan 250014, ChinaIn this paper, we assume that the reserve level of an insurance company can only be observed at discrete time points, then a new risk model is proposed by introducing a periodic capital injection strategy and a barrier dividend strategy into the classical risk model. We derive the equations and the boundary conditions satisfied by the Gerber-Shiu function, the expected discounted capital injection function and the expected discounted dividend function by assuming that the observation interval and claim amount are exponentially distributed, respectively. Numerical examples are also given to further analyze the influence of relevant parameters on the actuarial function of the risk model.https://www.mdpi.com/2227-7390/8/4/511compound Poisson risk modelperiodic capital injection strategyperiodic barrier dividend strategyGerber-Shiu functionexpected discounted dividend functionexpected discounted capital injection function |
| spellingShingle | Wenguang Yu Peng Guo Qi Wang Guofeng Guan Qing Yang Yujuan Huang Xinliang Yu Boyi Jin Chaoran Cui On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model Mathematics compound Poisson risk model periodic capital injection strategy periodic barrier dividend strategy Gerber-Shiu function expected discounted dividend function expected discounted capital injection function |
| title | On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model |
| title_full | On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model |
| title_fullStr | On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model |
| title_full_unstemmed | On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model |
| title_short | On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model |
| title_sort | on a periodic capital injection and barrier dividend strategy in the compound poisson risk model |
| topic | compound Poisson risk model periodic capital injection strategy periodic barrier dividend strategy Gerber-Shiu function expected discounted dividend function expected discounted capital injection function |
| url | https://www.mdpi.com/2227-7390/8/4/511 |
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