正则变化场合常数利息力度的破产概率

研究了常数利息力度下的破产概率.在索赔来到过程为更新过程,索赔额分布为Pareto型的场合下,得到了有限索赔次数破产概率的渐进表达公式.该结果推广了Kluppelberg和Stadtmuller(1998)和Qihe Tang(2005)的结果.     

一类相依索赔风险模型的破产概率问题研究

考虑一种相依索赔风险模型,其中每次索赔发生时根据索赔额的大小可随机产生一延迟的副索赔.采用L ap lace变换方法,给出了索赔额服从轻尾分布时的最终破产概率,并研究了重尾分布时最终破产概率的极限上下界.     

常息力更新场合有限时间破产概率对负相依索赔额的不敏感性

设索赔来到过程为具有常数利息力度的更新风险模型.在索赔额分布为负相依的次指数分布假定下,建立了有限时间破产概率的一个渐近等价公式.所得结果显示,在独立同分布索赔额情形,有限时间破产概率的有关渐近等价公式,在负相依场合依然成立.这表明有限时间破产概率对于索赔额的负相依结构是不敏感的.     

一类索赔为复合Poisson-Geometric过程双险种风险模型的破产概率

对索赔为复合Poisson-Geometric过程的双险种风险模型进行研究,给出了当初始资本为0及索赔额为指数分布下破产概率的具体表达式,并利用鞅方法得到了最终破产概率满足的Lundberg不等式和一般公式.     

一类索赔相依二元风险模型的破产概率问题研究

考虑一种相依索赔风险模型,模型中假设每次主索赔可随机产生一延迟的副索赔,采用Laplacc变换方法,给出了索赔额服从轻尾分布时的最终破产概率,并研究了重尾分布时最终破产概率的渐进式.     

随机保费下扰动风险模型总索赔盈余的大偏差

考虑随机保费下带干扰的风险模型,其中保费额和索赔额各自形成了END的随机变量序列,保费次数是由一个拟更新过程描绘,干扰项是由一个布朗运动过程来刻画.在索赔额分布属于一致变化类的条件下,给出了总索赔盈余过程的精致大偏差.     

一类索赔额服从指数幂尾型分布的风险模型及其破产概率的渐近性质

本文研究了一类风险模型,其个体索赔额服从指数-幂尾型分布,索赔次数过程为一更新过程,其更新时间间隔服从指数族分布；给出了这类模型在有限时间内破产概率的渐近性质；并讨论了在破产发生后的特征．     

考虑一般投资收益和时间相依索赔情形下二维带扰动风险模型的有限时间破产概率渐近估计

考虑具有一般投资收益过程的二维带扰动保险风险模型,假定保险公司盈余的投资收益过程由右连左极随机过程刻画,且两种索赔额与索赔到达时间间隔服从S armanov相依结构.当索赔额分布属于正则变化尾分布族时,得到有限时间破产概率的渐近公式.当描述投资收益过程的右连左极过程分别取Lévy过程,Vasicek利率模型,Cox-Ingersoll-Ross(CIR)利率模型,Heston模型时,得到相应投资收益情形下破产概率的渐近公式.     

相依风险模型的破产概率

本文研究了索赔额和索赔时间间隔相依的风险模型,得到了生存概率的表达式和最终破产概率表达式,并通过生存概率满足的积分微分方程求出了最终破产概率的Laplace-Stieltjes变换.     

改进后的复合Poisson-Geometric风险模型Gerber-Shiu折现惩罚函数

在考虑到因保费收入和通货膨胀等随机干扰的影响,以及将多余资本用于投资来提高赔付能力的基础上,文章对复合Poisson-Geometric风险模型做进一步推广,建立以保费收入服从复合Poisson过程,理赔量服从复合Poisson-Geometric过程的带投资的干扰风险模型,针对该风险模型,应用全期望公式,推导了Gerber-Shiu折现惩罚函数满足的更新方程,进而得到了在破产时盈余惩罚期望,破产赤字和破产概率满足的更新方程.并以保费额和索赔额均服从指数分布为例,给出破产概率满足的微分方程.以及通过数值例子,分析了初始准备金额,投资金额及保费额等对保险公司最终破产概率的影响.结论为经营者或决策者对各种金融或保险风险进行定量分析和预测提供了理论依据.     

Risk model with fuzzy random individual claim amount

In this paper, we consider a risk model in which individual claim amount is assumed to be a fuzzy random variable and the claim number process is characterized as a Poisson process. The mean chance of the ultimate ruin is researched. Particularly, the expressions of the mean chance of the ultimate ruin are obtained for zero initial surplus and arbitrary initial surplus if individual claim amount is an exponentially distributed fuzzy random variable. The results obtained in this paper coincide with those in stochastic case when the fuzzy random variables degenerate to random variables. Finally, two numerical examples are presented.     

复合Poisson-Geometric风险模型Gerber-Shiu折现惩罚函数

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.     

Ruin probabilities in the risk process with random income

We extend the classical risk model to the case in which the premium income process, modelled as a Poisson process, is no longer a linear function. We derive an analog of the Beekman convolution formula for the ultimate ruin probability when the inter-claim times are exponentially distributed. A defective renewal equation satisfied by the ultimate ruin probability is then given. For the general inter-claim times with zero-truncated geometrically distributed claim sizes, the explicit expression for the ultimate ruin probability is derived.     

On the discrete-time compound renewal risk model with dependence

In this paper, we study the discrete-time renewal risk model with dependence between the claim amount random variable and the interclaim time random variable. We consider several dependence structures between the claim amount random variable and the interclaim time random variable. Recursive formulas are derived for the probability mass function and the moments of the total claim amount over a fixed period of time. In the context of ruin theory, explicit expressions for the expected penalty (Gerber-Shiu) function are derived for special cases. We also discuss how the discrete-time compound renewal risk model with dependence can be used to approximate the corresponding continuous time compound renewal risk model with dependence. Numerical examples are provided to illustrate different topics discussed in the paper.     

带马氏利率的离散时间风险模型的破产概率

本文考虑一类保费和理赔额均为随机变量,且利率为马氏链的离散时间风险模型。推出了有限时间和最终时间破产概率的递归方程,并用归纳法得到了最终时间破产概率的上界表达式。     

Ruin probability in a one-sided linear model with constant interest rate

This paper investigates the ruin probability of a generalized renewal model with a constant interest rate, in which a one-sided linear model is used for the dependent claim process. An explicit asymptotic formula and an exponential upper bound are obtained for the ruin probability.     

Asymptotic finite-time ruin probability for a bidimensional renewal risk model with constant interest force and dependent subexponential claims

This paper considers a bidimensional renewal risk model with constant interest force and dependent subexponential claims. Under the assumption that the claim size vectors form a sequence of independent and identically distributed random vectors following a common bivariate Farlie–Gumbel–Morgenstern distribution, we derive for the finite-time ruin probability an explicit asymptotic formula.     

马氏环境下带扰动的变利率模型的风险理论

本文研究马氏环境下带扰动的变利率的Cox风险模型．证明了该模型的最终生存概率(或最终破产概率)满足一定的瑕疵更新方程．并利用更新理论给出了其Cramer-Lundberg渐近性质。本文还推导出最终生存概率(或最终破产概率)的卷积公式，从而推广了文献[1]的相应结果。     

索赔为稀疏过程的双复合 Poisson风险模型

研究了一类风险过程,其中保费收入为复合Poisson过程,而描述索赔发生的计数过程为保单到达过程的p-稀疏过程.给出了生存概率满足的积分方程及其在指数分布下的具体表达式,得到了破产概率满足的Lundberg不等式、最终破产概率及有限时间内破产概率的一个上界和生存概率的积分-微分方程,且通过数值例子,分析了初始准备金、保费收入、索赔支付及保单的平均索赔比例对保险公司破产概率的影响.