| 随机收益环境下的破产时刻罚金折现期望 |
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| 引用本文： | 李丽丽,冯敬海,宋立新. 随机收益环境下的破产时刻罚金折现期望[J]. 数学研究及应用, 2010, 30(2): 309-318. DOI: 10.3770/j.issn:1000-341X.2010.02.014 |
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| 作者姓名： | 李丽丽 冯敬海 宋立新 |
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| 作者单位： | 大连理工大学应用数学系, 辽宁 大连 116024;大连理工大学应用数学系, 辽宁 大连 116024;大连理工大学应用数学系, 辽宁 大连 116024 |
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| 基金项目： | 国家社科基金重大项目(Grant No.06&ZD039),大连理工大学``数学+X'项目. |
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| 摘 要： | This paper considers the expected discounted penalty function Φ(u) for the perturbed compound Poisson risk model with stochastic return on investments. After presenting an integro-differential equation that the expected discounted penalty function satisfies, the paper derives the closed form solution by constructing an identical equation. The exact expression for Φ (0) is given using the Laplace transform technique when interest rate is constant. Applications of the results are given to the ruin probability and moments of the deficit at ruin.
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| 关 键 词： | 罚金折现期望 投资回报 风险过程 随机 Laplace 积分微分方程 破产概率 风险模型 |
| 收稿时间： | 2008-03-21 |
| 修稿时间： | 2008-07-04 |
On the Expected Discounted Penalty Function for a Risk Process with Stochastic Return on Investments |
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| Li Li LI,Jing Hai FENG and Li Xin SONG. On the Expected Discounted Penalty Function for a Risk Process with Stochastic Return on Investments[J]. Journal of Mathematical Research with Applications, 2010, 30(2): 309-318. DOI: 10.3770/j.issn:1000-341X.2010.02.014 |
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| Authors: | Li Li LI Jing Hai FENG Li Xin SONG |
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| Affiliation: | School of Mathematical Sciences,Dalian University of Technology,Liaoning 116024,P.R.China |
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| Abstract: | This paper considers the expected discounted penalty function $Phi(u)$ for the perturbed compound Poisson risk model with stochastic return on investments. After presenting an integro-differential equation that the expected discounted penalty function satisfies, the paper derives the closed form solution by constructing an identical equation. The exact expression for $Phi'(0)$ is given using the Laplace transform technique when interest rate is constant. Applications of the results are given to the ruin probability and moments of the deficit at ruin. |
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| Keywords: | expected discounted penalty function integro-differential equation Laplace transform ruin. |
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