| 申海燕，周国立*.带扰动的延迟对偶风险模型的渐近解[J].海南师范大学学报自科版,2021,34(2):124-132 |
| 带扰动的延迟对偶风险模型的渐近解 |
| Asymptotics for a Delayed Dual Risk Model with Diffusion |
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| DOI：10.12051/j.issn.1674-4942.2021.02.002 |
| 中文关键词: 对偶风险模型 延迟时间 扰动过程 |
| 英文关键词: dual risk model delay time diffusion process |
| 基金项目:重庆市自然科学基金项目（cstc2020jcyj-msxm2554） |
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| 摘要点击次数: 533 |
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| 中文摘要: |
| 本研究将延迟和扰动同时引入对偶风险模型中，讨论了带一般Levy过程扰动的延迟对
偶风险模型。主要通过构造几类特殊函数，结合Ito公式和积分-偏微分方程等工具，得到了破产概
率和破产时间期望值的渐近解。然后在延迟时间为有界的条件下推导出了破产概率的显示解。
最后进行了数值模拟研究，模拟结果显示该模型下的破产概率比延迟对偶风险模型下的破产概率
更大。 |
| 英文摘要: |
| In this paper, the delay and diffusion were introduced into the dual risk model and the delayed dual risk model
with diffusion was discussed. By constructing some special functions and combining with Ito formula and integro-partial dif⁃
ferential equation, the asymptotic solutions of the ruin probability and the expectation of ruin time were obtained. Assuming
the delay time is bounded, explicit expressions of the ruin probability were obtained. Finally, a simulation study was carried
out in this paper. The simulation results show that the ruin probability in the delayed dual risk model with diffusion is big⁃
ger than the delayed dual risk model. |
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