带分红的稀疏风险模型的期望折现罚金函数  

Discounted penalty function for a thinning risk model with dividend

作　　者：陈洁[1] 吕玉华[2] 

机构地区：[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

出　　处：《山东大学学报（理学版）》2015年第9期78-83,共6页Journal of Shandong University(Natural Science)

基　　金：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。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.

关 键 词：稀疏 障碍分红 期望折现罚金函数 积分微分方程 拉普拉斯变换 

分 类 号：O211.6[理学—概率论与数理统计]