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.     

重尾索赔下带干扰风险模型破产概率的等价式

Embrechts—Goldie-Veraverbeke公式给出了在重尾索赔Cramer-Lundberg风险模型下关于破产概率的等价式．本文将上述风险模型推广到带干扰的Cramer-Lundberg风险模型,研究了索赔分布时破产概率的等价关系式．     

一般相依索赔离散风险模型的破产概率渐近估计及数值模拟

研究一类具有利率和相依索赔额的离散风险模型.在模型中,索赔额服从具有独立同分布步长的单边线性过程,贴现因子具有关于利率与时间的一般函数形式.在步长服从重尾分布的条件下,得到了最终破产概率的渐近估计.并通过具体实例分析利率对破产概率的影响.     

重尾索赔下双复合Poisson模型的赤字分布

本文研究重尾索赔下的双复合Poisson模型,当索赔额分布属于次指数分布类时,给出了破产在有限时间内发生赤字尾概率的一个渐近表达式.     

复合更新风险模型下的破产概率

讨论了具有较一般意义的复合更新风险模型下的破产概率,在假定索赔分布属于重尾分布族的前提下,得到了我们所渴望的破产概率的尾等价形式.这一结果恰与经典的Cram啨r-Lundberg模型下的结论相一致.     

离散的相依风险模型的破产问题

研究一类索赔时间相依的离散风险模型,模型中假设每次主索赔可能引起一次副索赔,而每次副索赔有可能延迟发生.通过引入辅助模型,运用概率论的分析方法得到了破产前瞬时盈余和破产时赤字联合分布的递推解,以及初始值为0时最终破产概率的明确表达式.最后结合保险实例进行了数值模拟.     

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．     

一类相依索赔离散风险模型的有限时间破产概率估计

本文研究一类具有相依索赔及重尾索赔噪声项的离散风险模型有限时间破产概率.在该模型中,索赔额服从具有独立同分布噪声项的单边线性过程;由保险公司的风险投资和无风险投资导致的随机折现因子与单边线性过程的噪声项相独立;保险公司的保费率是恒定的常数.当单边线性过程的噪声项服从重尾分布时,本文得到该离散风险模型有限时间破产概率的渐近估计.     

依生灭过程索赔两险种风险模型

本文建立了依生灭过程索赔的两险种风险模型,主要对该模型的破产概率进行了研究,并给出了关于条件破产概率序列的微分积分方程以及破产概率收敛速率的上界,这类似于Cramer-Lundberg逼近,其逼近程度虽然不如Cramer-Lundberg逼近"精确",但不要求索赔额分布是尾指数的.     

基于相依风险模型破产概率的渐近估计及其实证分析

本文研究了重尾相依风险模型,其中索赔额是一列上广义负相依随机变量,索赔时间间隔是—列广义负相依随机变量,并且两个序列是相互独立的,得到了保险公司最终破产概率的渐近结果。并且利用中国人民财产保险股份有限公司2008年的重大赔付数据,对该公司的最终破产概率进行了实证分析。     

变保费率Cox风险模型的研究

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.     

具有两种副索赔的离散相依风险模型破产问题

考虑了一类离散相依的风险模型,该模型假设主索赔以一定的概率引起两种副索赔,而第一种副索赔有可能延迟发生.通过引入一个辅助模型,分别得出了该风险模型初始盈余为0时破产前盈余与破产时赤字的联合分布的表达式、初始盈余为"时破产前盈余和破产时赤字的联合分布的递推公式、初始盈余为0时的破产概率,以及初始盈余为"时的破产概率求解方...     

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.     

The compound Poisson risk model with dependence under a multi-layer dividend strategy

In this paper, a compound Poisson risk model with time-dependent claims is studied under a multi-layer dividend strategy. A piecewise integro-differential equation for the Gerber-Shiu function is derived and solved. Asymptotic formulas of the ruin probability are obtained when the claim size distributions are heavy-tailed.     

On the decomposition of the absolute ruin probability in a perturbed compound Poisson surplus process with debit interest

We consider a compound Poisson surplus process perturbed by diffusion with debit interest. When the surplus is below zero or the company is on deficit, the company is allowed to borrow money at a debit interest rate to continue its business as long as its debt is at a reasonable level. When the surplus of a company is below a certain critical level, the company is no longer profitable, we say that absolute ruin occurs at this situation. In this risk model, absolute ruin may be caused by a claim or by oscillation. Thus, the absolute ruin probability in the model is decomposed as the sum of two absolute ruin probabilities, where one is the probability that absolute ruin is caused by a claim and the other is the probability that absolute ruin is caused by oscillation. In this paper, we first give the integro-differential equations satisfied by the absolute ruin probabilities and then derive the defective renewal equations for the absolute ruin probabilities. Using these defective renewal equations, we derive the asymptotical forms of the absolute ruin probabilities when the distributions of claim sizes are heavy-tailed and light-tailed. Finally, we derive explicit expressions for the absolute ruin probabilities when claim sizes are exponentially distributed.     

On a correlated aggregate claims model with Poisson and Erlang risk processes

In this paper we consider a risk model with two dependent classes of insurance business. In this model the two claim number processes are correlated. Claim occurrences of both classes relate to Poisson and Erlang processes. We derive explicit expressions for the ultimate survival probabilities under the assumed model when the claim sizes are exponentially distributed. We also examine the asymptotic property of the ruin probability for this special risk process with general claim size distributions.     

更新模型中的Schmitter问题

Schmitter问题是指在期望和方差固定的条件下，求出使得破产概率最大（小）的索赔分布，F．De Vylder讨论了古典风险模型的情况，本文讨论了更新风险模型的情况，推广了其结果。     

具有Vasicek利率的风险过程的破产概率的分解(英文)

In this paper, it is assumed that an insurer with a jump-diffusion risk process would invest its surplus in a bond market, and the interest structure of the bond market is assumed to follow the Vasicek interest model. This paper focuses on the studying of the ruin problems in the above compounded process. In this compounded risk model, ruin may be caused by a claim or oscillation. We decompose the ruin probability for the compounded risk process into two probabilities： the probability that ruin caused by a claim and the probability that ruin caused by oscillation. Integro-differential equations for these ruin probabilities are derived. When the claim sizes are exponentially distributed, the above-mentioned integro-differential equations can be reduced into a three-order partial differential equation.