一类时间相依复合更新风险模型损失过程的尾概率渐近估计

考虑一类复合相依更新风险模型,一次事故引发多次索赔.假设索赔次数与索赔时刻相依,同一事故引起的索赔额是宽上限相依(widely upper orthant dependent)且服从重尾分布.得到该风险模型损失过程的精细大偏差和有限时破产概率的渐近估计.     

重尾索赔下的一类相依风险模型的若干问题

本文研究了重尾索赔下的一类相依风险模型,得到了破产概率的尾等价式及索赔盈余过程大偏差的渐近关系式.在该模型中,一索赔到达过程是Poisson过程,另一索赔到达过程为其p-稀疏过程.     

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.     

一类相依双险种风险模型的罚金折现期望函数

考虑索赔到达具有相依性的一类双险种风险模型,其中第一类险种的索赔计数过程为Poisson过程,第二类险种的索赔计数过程为其p-稀疏过程与广义Erlang(2)过程的和,利用更新论证得到了此风险模型的罚金折现期望函数满足的微积分方程及其Laplace变换的表达式.并就索赔额均服从指数分布的情形,给出了罚金函数及破产概率的精确表达式.     

一类相依风险模型的破产问题

本文研究了一类索赔过程与索赔额大小相关的风险模型.利用无穷小方法,得到了该相依模型的折扣惩罚函数的期望满足的方程.及其拉普拉斯变换的表达式.并且给出指数索赔时的具体运用.     

二元复合Poisson风险模型的几个结果

本文研究具有相依关系的一类风险模型.得到了由不同类别的索赔产生的破产时赤字分布的渐近结果以及指数索赔下的精确结果.同时研究了带伽玛过程干扰的古典风险过程.     

广义负相依一般风险模型中有限时破产概率的估计及数值模拟

本文研究了一类带利率的重尾相依风险模型, 其中索赔额是一列上广义负相依随机变量, 索赔到达过程是一般的非负整值过程, 并且独立于索赔额序列, 保费收入过程是一个一般的非负非降随机过程. 我们考虑了两种情况, 其一是索赔额、索赔到达过程及保费收入过程相互独立, 其二是累积折现保费收入总量的尾概率可以被索赔额的尾概率高阶控制, 得到了保险公司有限时破产概率的渐近估计,并且给出了相应的数值模拟, 验证了理论结果的合理性.     

ON THE CRAM(E)R-LUNDBERG RISK MODEL WITH A CONSTANT FORCE OF INTEREST AND SURPLUS-DEPENDENT LOSS-CARRY-FORWARD TAX STRUCTURE

本文研究了带常数利率和盈余相依型loss-carry-forward税收系统的Cramér-Lundberg风险模型.利用无穷小分析方法及该过程具有的的强马氏性,得出了保险公司从开始运营到破产期间税收折现总额的数学期望表达式.作为例子,本文给出了指数分布索赔假定下该税收折现函数的具体表达式.     

关于带常数利率与盈余相依型loss-carry-forward税收系统的Cramr-Lundberg风险模型(英文)

本文研究了带常数利率和盈余相依型loss-carry-forward税收系统的Cramr-Lundberg风险模型.利用无穷小分析方法及该过程具有的的强马氏性,得出了保险公司从开始运营到破产期间税收折现总额的数学期望表达式.作为例子,本文给出了指数分布索赔假定下该税收折现函数的具体表达式.     

考虑随机投资收益和单边线性索赔的时间依赖更新风险模型的破产概率

本文主要研究一类考虑随机投资收益和相依索赔额的时间依赖的更新风险模型.在该模型中,保险投资收益服从指数Lévy过程,而索赔额服从具有独立同分布步长的单边线性过程.该单边线性过程的步长与索赔到达时间构成独立同分布的随机向量序列,并且该随机向量的分量之间具有运用步长关于索赔到达时间间隔的条件尾概率渐近性刻画的相依关系.当单边线性过程的步长服从重尾分布时,本文得到该更新风险模型破产概率在时间域内的一致渐近估计.     

Moments of claims in a Markovian environment

This paper considers discounted aggregate claims when the claim rates and sizes fluctuate according to the state of the risk business. We provide a system of differential equations for the Laplace–Stieltjes transform of the distribution of discounted aggregate claims under this assumption. Using the differential equations, we present the first two moments of discounted aggregate claims in a Markovian environment. We also derive simple expressions for the moments of discounted aggregate claims when the Markovian environment has two states. Numerical examples are illustrated when the claim sizes are specified.     

马尔可夫环境下聚合索赔的前二阶矩

We consider the discounted aggregate claims when the insurance risks and financial risks are governed by a discrete-time Markovian environment.We assume that the claim sizes and the financial risks fluctuate over time according to the states of economy,which are interpreted as the states of Markovian environment.We will then determine a system of differential equations for the Laplace-Stieltjes transform of the distribution of discounted aggregate claims under mild assumption.Moreover,using the differentio-integral equation,we will also investigate the first two order moments of discounted aggregate claims in a Markovian environment.     

The asymptotic estimate for the sum of two correlated classes of discounted aggregate claims with heavy tails

Consider a risk model with two correlated classes of insurance business and a constant force of interest. We assume that the correlation comes from a common shock and that the claim-size distribution is heavy-tailed. Under this setting, we investigate the tail behavior of the sum of the two correlated classes of discounted aggregate claims. We obtain the uniform asymptotic formulas for some subclass of subexponential distributions.     

一类索赔相关风险模型破产概率的研究

本文讨论一类索赔相关同时保费收取为一复合泊松过程的风险模型的破产问题，给出相应的Lundberg不等式．     

On the numerical evaluation of the distribution of aggregate claims and its stop-loss premiums

The paper develops a method for the numerical evaluation of the distribution of aggregate claims and its stop-loss premiums.     

不完全市场的保险定价研究

完全市场上的保险定价问题是人们比较熟悉的研究内容,但它不符合市场实际.本文在不完全市场上研究保险定价的问题.通过对累积保险损失的分析,建立在累积赌付下的保险定价模型;基于对一个无风险资产和有限多个风险资产的投资,建立保险投资定价模型.通过变形,得到相应的保险价格的倒向随机微分方程,并利用倒向随机微分方程的理论和方法,得到了相应的保险价格公式.最后,给出释例进行了分析.本文的研究,不用考虑死亡率、损失的概率分布等因素,为保险定价提供了新的思路,丰富了有限的保险定价方法.     

Moments of discounted aggregate claim costs until ruin in a Sparre Andersen risk model with general interclaim times

In the context of a Sparre Andersen risk model with arbitrary interclaim time distribution, the moments of discounted aggregate claim costs until ruin are studied. Our analysis relies on a novel generalization of the so-called discounted density which further involves a moment-based component. More specifically, while the usual discounted density contains a discount factor with respect to the time of ruin, we propose to incorporate powers of the sum until ruin of the discounted (and possibly transformed) claims into the density. Probabilistic arguments are applied to derive defective renewal equations satisfied by the moments of discounted aggregate claim costs until ruin. Detailed examples concerning the discounted aggregate claims and the number of claims until ruin are studied upon assumption on the claim severities. Numerical illustrations are also given at the end.     

一类推广的复合Poisson-Geometric相依风险模型的破产概率

研究了一类推广的复合Poisson—Geometric风险相依模型．利用盈余过程的鞅性,得到了破产概率公式以及破产概率所满足的积分方程和Cramer—Lundberg逼近．最后给出了索赔额服从指数分布时Cramer-Lundberg逼近的精确表达式．     

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??This paper studies the distribution of finite-time ruin quantities. It gives the probability mass function of finite time number of claims, and find the distribution function of aggregate claims by using discretise method and compared with exact distribution function, which shows that the approximation works very well. In addition, by applying decomposition for density function, it gives the explicit expression for joint density of ruin time and deficit at ruin.