兰州大学机构库 >数学与统计学院
阈红利策略下复合Poisson风险模型的绝对破产
Alternative TitleAbsolute ruin in the compound Poisson risk model
李文婷
Thesis Advisor牛明飞
2010-05-22
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword绝对破产 Gerber-Shiu折现罚金函数 阈红利策略 积分微分方程 红利折现期望
Abstract绝对破产是指当盈余额小于零时,保险公司可以通过向银行贷款等融资手段来弥补暂时的赤字,继续经营.而当公司债务或者负盈余低于某一特定值时,保险公司已经无力通过保费收入使盈余为正,这时称绝对破产发生了. 本文基于此意义,考虑了带有阈红利策略的复合Poisson风险模型的破产问题,得到了Gerber-Shiu折现罚金函数所满足的积分微分方程和在破产前红利折现期望所满足的积分微分方程.最后,推导了当理赔额服从指数分布时,期望折现罚金函数所满足的具体的表达式,并给出了这一情况下的绝对破产概率 (u,b)所满足的积分微分方程.
Other AbstractAbsolute ruin means that when the surplus process is below zero, the insurer could borrow money at a debit interest rate to continue her business. Mean while the insurer will repay the debts from her premium income. We assume that an insurer is allowed to continue her business with debts until her debts or negative surplus is below some certain level, and in the latter case, the insurer is no longer allowed to run her business, absolute ruin occurs at this situation. By this means, in the present paper, we investigate the absolute ruin problem in the compound Poisson risk model with threshold dividend strategy. We first derive integro-differential equations for the expected discounted value of all dividends until absolute ruin and expected discounted penalty function. In the case of exponential claim amounts, we obtain explicit expressions for m(u;b)and absolute ruin probability.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/224373
Collection数学与统计学院
Recommended Citation
GB/T 7714
李文婷. 阈红利策略下复合Poisson风险模型的绝对破产[D]. 兰州. 兰州大学,2010.
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