稀疏过程下保费与理赔相关的风险模型的破产概率

J4 ›› 2011, Vol. 46 ›› Issue (7): 56-59.

稀疏过程下保费与理赔相关的风险模型的破产概率

黄玉娟¹, 于文广²

1. 山东交通学院数理系, 山东济南 250023; 2. 山东经济学院统计与数学学院, 山东济南 250014

收稿日期:2010-12-13 出版日期:2011-07-20 发布日期:2011-09-08
通讯作者: 于文广(1977- ),男,汉族,副教授, 主要研究领域为金融数学, 随机控制及其应用, G期望及其应用. Email: yuwg@mail.sdu.edu.cn
作者简介:黄玉娟(1977- ),女,汉族,讲师,主要研究领域为保险风险管理与精算.Email: yujuanh518@163.com
基金资助:
教育部人文社会科学研究基金资助项目(10YJC630092; 09YJC910004); 山东省自然科学基金资助项目(ZR2010GL013); 山东省高校人文社会科学研究计划资助项目(J10WF84);山东交通学院自然科学基金资助项目(Z201031)

Ruin probability for a risk model with dependence between premium and claim under the thinning process

HUANG Yu-juan¹, YU Wen-guang²

1. Department of Mathematics and Physics, Shandong Jiaotong University, Jinan 250023, Shandong, China;
2. School of Statistics and Mathematics, Shandong Economic University, Jinan 250014, Shandong, China

Received:2010-12-13 Online:2011-07-20 Published:2011-09-08

摘要/Abstract

摘要：

考虑了一类相依结构的风险模型, 其中索赔产生时依概率ρ的可能性同时产生一次续保,即续保过程是索赔的ρ稀疏过程。同时还研究了资金利率、通货膨胀率和干扰问题。通过鞅分析方法,得到了最终破产概率的一般表达式和破产概率的一个上界估计, 讨论了相应模型的调整系数方程和调节系数的上下界。

关键词: 破产概率;调节系数;稀疏过程;鞅;扰动

Abstract:

A dependence risk model is considered, where the claim may produce a repremium with probability ρ, i.e. the repremium process is the ρ-thinning process of the claim process. The capital interest rate, inflatable rate and diffusion are also investigated. Then by the method of martingle analysis, the estimation of upper bond and general formula of the the ultimate ruin probability in this new model are got. In addition adjustment coefficient equation is established and the upper bond and lower bond of the adjustment coefficients are estimated.

Key words: ruin probabilties; adjuist coefficent; thinning process; martingle; diffusion

黄玉娟1, 于文广2. 稀疏过程下保费与理赔相关的风险模型的破产概率[J]. J4, 2011, 46(7): 56-59.

HUANG Yu-juan1, YU Wen-guang2. Ruin probability for a risk model with dependence between premium and claim under the thinning process[J]. J4, 2011, 46(7): 56-59.

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