Ruin Probability in Compound Poisson Process with Investment
We consider that the surplus of an insurer follows compound Poisson process and the insurer would invest its surplus in risky assets, whose prices satisfy the Black-Scholes model. In the risk process, we decompose the ruin probability into the sum of two ruin probabilities which are caused by the cl...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/286792 |
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| _version_ | 1850174971120189440 |
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| author | Yong Wu Xiang Hu |
| author_facet | Yong Wu Xiang Hu |
| author_sort | Yong Wu |
| collection | DOAJ |
| description | We consider that the surplus of an insurer follows compound Poisson process and the insurer would invest its surplus in risky assets, whose prices satisfy the Black-Scholes model. In the risk process, we decompose the ruin probability into the sum of two ruin probabilities which are caused by the claim and the oscillation, respectively. We derive the integro-differential equations for these ruin probabilities these ruin probabilities. When the claim sizes are exponentially distributed, third-order differential equations of the ruin probabilities are derived from the integro-differential equations and a lower bound is obtained. |
| format | Article |
| id | doaj-art-d6896bd4fde547fa92f2353a22052aff |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-d6896bd4fde547fa92f2353a22052aff2025-08-20T02:19:33ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/286792286792Ruin Probability in Compound Poisson Process with InvestmentYong Wu0Xiang Hu1School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, ChinaSchool of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, ChinaWe consider that the surplus of an insurer follows compound Poisson process and the insurer would invest its surplus in risky assets, whose prices satisfy the Black-Scholes model. In the risk process, we decompose the ruin probability into the sum of two ruin probabilities which are caused by the claim and the oscillation, respectively. We derive the integro-differential equations for these ruin probabilities these ruin probabilities. When the claim sizes are exponentially distributed, third-order differential equations of the ruin probabilities are derived from the integro-differential equations and a lower bound is obtained.http://dx.doi.org/10.1155/2012/286792 |
| spellingShingle | Yong Wu Xiang Hu Ruin Probability in Compound Poisson Process with Investment Journal of Applied Mathematics |
| title | Ruin Probability in Compound Poisson Process with Investment |
| title_full | Ruin Probability in Compound Poisson Process with Investment |
| title_fullStr | Ruin Probability in Compound Poisson Process with Investment |
| title_full_unstemmed | Ruin Probability in Compound Poisson Process with Investment |
| title_short | Ruin Probability in Compound Poisson Process with Investment |
| title_sort | ruin probability in compound poisson process with investment |
| url | http://dx.doi.org/10.1155/2012/286792 |
| work_keys_str_mv | AT yongwu ruinprobabilityincompoundpoissonprocesswithinvestment AT xianghu ruinprobabilityincompoundpoissonprocesswithinvestment |