带利息力和干扰的批量索赔一般到达风险模型

本文在经典风险模型的基础上,将索赔到达过程推广为更新过程,索赔可以批量到达,且带有常数利息力和Brown运动干扰项,得到一个新的风险模型,运用Markov骨架过程的方法,得出盈余过程的瞬时分布和生存概率.     

NCD系统的数学建模与稳态分析

本文以有限齐次马尔科夫链对NCD（无索赔折扣）系统建模，严谨地证明了，任一NCD系统皆存在唯一的平稳分布。此外，给出了求解这一平稳分布的一般算法，并揭示了此平稳分布的结构。特别地，对两类给定的折扣类转移法则，还给出了平稳分布的显式。     

Bivariate Recursive Equations on Excess-of-loss Reinsurance

This paper investigates bivariate recursive equations on excess-of-loss reinsurance. For an insurance portfolio, under the assumptions that the individual claim severity distribution has bounded continuous density and the number of claims belongs to R1 （a, b） family, bivariate recursive equations for the joint distribution of the cedent＇s aggregate claims and the reinsurer＇s aggregate claims are obtained.     

Asymptotic estimates of Gerber-Shiu functions in the renewal risk model with exponential claims

This paper continues to study the asymptotic behavior of Gerber-Shiu expected discounted penalty functions in the renewal risk model as the initial capital becomes large. Under the assumption that the claim-size distribution is exponential, we establish an explicit asymptotic formula. Some straightforward consequences of this formula match existing results in the field.     

RUIN PROBABILITY IN A SEMI-MARKOV RISK MODEL WITH CONSTANT INTEREST FORCE AND HEAVY-TAILED CLAIMS

In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.     

保单个数为Poisson分布的总理赔额分布函数的界值研究

根据单个保单理赔额分布函数F(z)的一些特殊性质,研究了开放个别风险模型在保单个数N为Poisson分布下,总理赔额分布函数F_S(x)对任意x(x≥0)的界值问题,得到一些实用的、便于数值计算的界值结果,具有重要的应用价值．     

索赔次数数据分布的拟合方法的分析和比较

泊松分布和负二项分布常用于拟合保险索赔次数.它们和二项分布统称为(a,b,0)分布族.本文对(a,b,0)分布族进行了研究,然后在此基础上给出了(a,b,0)分布离散型随机变量是服从泊松分布,还是服从负二项分布或二项分布的检验方法.本文基于我国某家保险公司的索赔次数数据进行了实证分析,并对检验的功效进行了模拟研究.     

负二项分布的优良特性及其在风险管理中的应用

孟生旺．负二项分布的优良特性及其在风险管理中的应用．数理统计与管理，１９９８，１７（２），９～１２．负二项分布之所以在风险管理中被广泛应用是由其优良特性所决定的。本文主要讨论了其中三个方面的问题：第一，负二项分布在描述风险集体中任意风险的索赔次数时表现为伽玛分布对泊松分布按参数变化的加权平均；第二，负二项分布在描述某些风险的累积索赔额时具有复合泊松分布的形式；第三，负二项分布是当风险的索赔频率强度之间存在正向传染时索赔次数的分布     

常利率下保费随马氏环境变化的风险模型的破产概率

破产概率受保费变化影响,保费随着准备金变化,在本文中考虑带有利率的风险模型;其索赔发生是Cox过程.     

Asymptotics of discounted aggregate claims for renewal risk model with risky investment

Under the assumption that the claim size is subexponentially distributed and the insurance surplus is totally invested in risky asset, a simple asymptotic relation of tail probability of discounted aggregate claims for renewal risk model within finite horizon is obtained. The result extends the corresponding conclusions of related references.