共查询到17条相似文献,搜索用时 140 毫秒
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研究了当保费率随理赔强度的变化而变化时C ox风险模型的折现罚金函数,利用后向差分法得到了折现罚金函数所满足的积分方程,进而得到了破产概率,破产前瞬时盈余、破产时赤字的各阶矩所满足的积分方程.最后给出当理赔额服从指数分布,理赔强度为两状态的马氏过程时破产概率的拉普拉斯变换,对一些具体数值计算出了破产概率的表达式. 相似文献
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索赔次数为复合Poisson-Geometric过程的常利率风险模型的罚金函数 总被引:3,自引:0,他引:3
讨论了常利率下索赔次数为复合Poisson-Geometric过程的风险模型的罚金函数,得到了罚金函数的期望所满足的积分方程,并由所得到的积分方程推出了破产概率所满足的积分方程,初始盈余为0时,得到了罚金函数的期望及破产概率的精确解. 相似文献
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本文研究了具有随机保费收入的风险模型的Gerber-Shiu罚金函数的可微性以及渐近性质,随机保费收入通过一个复合泊松过程刻画.本文得到了Gerber-Shiu函数所满足的积分微分方程,给出了Gerber-Shiu罚金函数二次可微与三次可微的充分条件.当所讨论的罚金函数是三次可微的时候,前述积分微分方程可以转化为一般的常微分方程.利用常微分方程的标准方法,当个体随机保费和随机理赔都是指数分布的时候,得到了绝对破产概率在初始盈余趋向于无穷大时的渐近性质. 相似文献
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本文研究了利率、保费均为随机变量的两个离散风险模型.利用递推的方法,得到了有限时间内的破产概率和最终破产概率所满足的积分方程,以及盈余首次穿过给定水平时刻的分布的递推公式,从而可以对保险公司各个破产指标得出数值结论. 相似文献
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本文考虑了当索赔间隔时间为Erlang(2)分布且保费收取为二步保费过程的复合更新风险模型,推导出该模型的罚金折现期望值函数满足具有一定边界条件和积分微分方程,并解出该方程.特别地,当索赔额为指数分布时,利用所得结果给出了破产时间的Laplace变换及终积破产概率的解析解. 相似文献
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具有随机保费风险模型破产概率的下界及渐近表示 总被引:1,自引:0,他引:1
本文研究一类推广的风险模型,其保费收入过程不再是时间的线性函数.利用寿命分布类D-NBU我们获得了破产概率的一些下界.利用破产概率所满足的一个更新方程,我们还得到了关于破产概率的一个渐近表达式. 相似文献
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考虑信用风险模型的破产问题,研究Gerber-Shiu贴现罚函数,通过引进辅助模型,运用概率论的分析方法得到了其所满足的积分方程.相应地可以得到该模型下的破产概率、破产时刻前赢余和破产时刻赤字的联合分布及其边际分布,进一步完善了YangHailiang发表的相关问题的结果. 相似文献
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Consider a compound Poisson surplus process of an insurer with debit interest and tax payments. When the portfolio is in a profitable situation, the insurer may pay a certain proportion of the premium income as tax payments. When the portfolio is below zero, the insurer could borrow money at a debit interest rate to continue his/her business. Meanwhile, the insurer will repay the debts from his/her premium income. The negative surplus may return to a positive level except that the surplus is below a certain critical level. In the latter case, we say that absolute ruin occurs. In this paper, we discuss absolute ruin quantities by defining an expected discounted penalty function at absolute ruin. First, a system of integro-differential equations satisfied by the expected discounted penalty function is derived. Second, closed-form expressions for the expected discounted total sum of tax payments until absolute ruin and the Laplace-Stieltjes transform (LST) of the total duration of negative surplus are obtained. Third, for exponential individual claims, closed-form expressions for the absolute ruin probability, the LST of the time to absolute ruin, the distribution function of the deficit at absolute ruin and the expected accumulated discounted tax are given. Fourth, for general individual claim distributions, when the initial surplus goes to infinity, we show that the ratio of the absolute ruin probability with tax to that without tax goes to a positive constant which is greater than one. Finally, we investigate the asymptotic behavior of the absolute ruin probability of a modified risk model where the interest rate on a positive surplus is involved. 相似文献
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本文推广了龚日朝(2001)的风险模型,把保费随机化,利用鞅方法讨论了保单来到过程与索赔来到过程均为Po isson过程的破产概率.接着又讨论了G erber-Sh iu期望折现函数,推导出了其满足的积分方程,以及L ap lace变换.最后利用随机游动的知识,讨论了当保单来到过程与索赔来到过程为同一更新过程时的破产概率. 相似文献
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文章考虑了复合Poisson-Geometic风险下带投资和障碍分红的Gerber-shiu函数问题,运用全期望公式得到了复合Poisson-Geometic风险下带投资和障碍分红的函数所满足的更新方程。并在指数分布的假设下,得到了带投资和障碍分红的保险公司的破产概率的显式表达,最后通过数值算例分析了风险模型的几个关键参数对破产概率的影响,验证了文章结果的合理性,同时也给保险公司的资金管理提出了指导意见。结果表明:充足的初始准备金、较低的赔付门槛、较高收益率的风险资产都是降低破产风险的重要策略。 相似文献
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In this paper, we consider a renewal risk process with random premium income based on a Poisson process. Generating function for the discounted penalty function is obtained. We show that the discounted penalty function satisfies a defective renewal equation and the corresponding explicit expression can be obtained via a compound geometric tail. Finally, we consider the Laplace transform of the time to ruin, and derive the closed‐form expression for it when the claims have a discrete Km distribution (i.e. the generating function of the distribution function is a ratio of two polynomials of order m∈?+). Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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复合Poisson-Geometric风险模型Gerber-Shiu折现惩罚函数 总被引:11,自引:0,他引:11
本文研究赔付为复合Poisson-Geometric过程的风险模型,首先得到了Gerber-Shiu折现惩罚期望函数所满足的更新方程,然后在此基础上推导出了破产概率和破产即刻前赢余分布等所满足的更新方程,再运用Laplace方法得出了破产概率的Pollazek-Khinchin公式,最后根据Pollazek-Khinchin公式,直接得出了当索赔分布服从指数分布的情形下破产概率的显示表达式. 相似文献
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Huai Xu & Ling Tang 《数学研究通讯:英文版》2012,28(4):349-358
In this paper, we consider a Gerber-Shiu discounted penalty function in
Sparre Andersen risk process in which claim inter-arrival times have a phase-type (2)
distribution, a distribution with a density satisfying a second order linear differential
equation. By conditioning on the time and the amount of the first claim, we derive
a Laplace transform of the Gerber-Shiu discounted penalty function, and then we
consider the joint density function of the surplus prior to ruin and the deficit at ruin
and some ruin related problems. Finally, we give a numerical example to illustrate
the application of the results. 相似文献