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| 带分红的稀疏风险模型的期望折现罚金函数 | |
| 引用本文： | 陈洁,吕玉华. 带分红的稀疏风险模型的期望折现罚金函数[J]. 山东大学学报(理学版), 2015, 50(9): 78-83. DOI: 10.6040/j.issn.1671-9352.0.2014.373 |
| 作者姓名： | 陈洁 吕玉华 |
| 作者单位： | 1. 济宁学院数学系, 山东 济宁 273155; 2. 曲阜师范大学数学科学学院, 山东 曲阜 273165 |
| 基金项目： | 国家自然科学基金资助项目(11171179);山东省自然科学基金资助项目(ZR2009AL015) |
| 摘 要： | 考虑一类带分红的稀疏风险模型,得到了期望折现罚金函数的积分微分方程。当保费额与索赔额同为指数分布时,研究了积分微分方程的拉普拉斯变换的解以及破产概率、赤字分布、破产时刻的瞬间盈余分布的积分微分方程的显解。 |
| 关 键 词： | 障碍分红 稀疏 拉普拉斯变换 期望折现罚金函数 积分微分方程 |
| 收稿时间： | 2014-08-14 |
Discounted penalty function for a thinning risk model with dividend |
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| CHEN Jie,L,#,Yu-hua. Discounted penalty function for a thinning risk model with dividend[J]. Journal of Shandong University, 2015, 50(9): 78-83. DOI: 10.6040/j.issn.1671-9352.0.2014.373 | |
| Authors: | CHEN Jie L&# Yu-hua |
| Affiliation: | 1. Department of Mathematics, Jining University, Jining 273155, Shandong, China; 2. School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China |
| Abstract: | The thinning risk model with barrier dividend was considered. The integro-differential equation for the expected discounted penalty function was obtained. If the premium and the claim sizes are exponentially distributed, some expressions for the Laplace transform of the integro-differential equation were founded. When the premium and the claim sizes are exponentially distributed, the closed-form solutions of the time of ruin, the deficit at ruin and the surplus before ruin were obtained. |
| Keywords: | barrier dividend Laplace transform integro-differential equation thinning process expected discounted penalty function |
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