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 |
随机收益环境下的破产时刻罚金折现期望 |
On the Expected Discounted Penalty Function for a Risk Process with Stochastic Return on Investments |
投稿时间:2008-03-21 修订日期:2008-07-04 |
DOI:10.3770/j.issn:1000-341X.2010.02.014 |
中文关键词: 破产时刻罚金折现期望 积分-微分方程 拉普拉斯变换 破产. |
英文关键词:expected discounted penalty function integro-differential equation Laplace transform ruin. |
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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中文摘要: |
本文在公司资产服从跳跃-扩散过程的风险模型下,讨论保险公司的破产问题. 在随机利率为带漂移的布朗运动的条件下,得到破产时刻罚金折现期望~$\Phi(u)$~所满足的方程与边界条件,并得到常利率环境下 ~$\Phi'(0)$~的精确解及~$\Phi(u)$~的解析表达式.最后利用~$\Phi(u)$ ~得到了破产概率和破产时刻的矩所满足的积分-微分方程. |
英文摘要: |
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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