带扩散扰动项的广义双Poisson风险模型下的破产概率

本文首先在[1]-[4]讨论的基础上,将经典的破产模型推广到带扩散扰动项的广义双Po isson风险模型,即将保费收取过程和索赔总额过程同时推广到广义复合Po isson过程,以此解决在同一时刻有两张以上保单到达和两个以上顾客索赔的实际问题;接着运用鞅方法证明了破产概率满足的Lundberg不等式和一般公式在我们所建的模型下同样成立.     

带干扰的复合广义齐次Poisson过程的多险种破产概率

将复合广义齐次poisson过程的多险种风险模型推广到带干扰的一种新模型,运用鞅方法破产概率满足的Lundberg不等式和一般公式.     

相关带干扰风险模型的破产概率

本文引进了含相关类带干扰经典风险过程, 研究类之间的相关性对破产概率的影响, 主要研究类之间的相关性对其Lundberg指数的大小关系的影响.     

Asymptotics for the Moments of the Time to Ruin for the Compound Poisson Model Perturbed by Diffusion

We obtain the asymptotic behaviour of the k-th moment of the time to ruin in the classical risk model perturbed by diffusion for the case where the claim size distribution has a heavy tail.     

带干扰的双Poisson风险模型的破产概率

首先将[3]的双Possion风险模型推广到带干扰的一种新模型。然后运用鞅论的方法得出破产概率满足Lundberg不等式和一般公式。以及当个体所赔服从指数分布时的破产概率的具体表达式。     

带干扰的多险种Cox风险模型的破产概率

考虑到保险公司在实际经营中收益所具有的不确定性和风险经营的多元化,建立了一个更现实的风险模型即带干扰的多险种Cox风险模型.运用鞅论得到了该模型最终破产概率的上界,并对Lundberg不等式作了推广.     

复合广义齐次Poisson过程的多险种破产概率

本文推广了经典的复合泊松风险模型，建立了两类复合广义齐次poisson过程的多险种破产模型．对于新模型，我们得到了初始资本为u的破产概率φ(u)的精确表达式以及特殊情况下φ(0)的表达式，并且导出了调节系数方程和调节系数R的上下界．     

Some Results for the Compound Poisson Process That Is Perturbed by Diffusion

Abstract In the present paper surplus process perturbed by diffusion are considered.The distributions ofthe surplus immediately before and at ruin corresponding to the probabilities of ruin caused by oscillation andruin caused by a claim are studied.Some joint distribution densities are obtained.Techniques from martingaletheory and renewal theory are used.     

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本文考虑了常利力下带干扰的双复合Poisson风险过程, 借助微分和伊藤公式, 分别获得了无限时和有限时生存概率的积分微分方程. 当保费服从指数分布时, 得到了无限时生存概率的微分方程.     

常利率下带干扰负风险和模型的破产概率

本文考虑了常利率下带干扰负风险和模型的破产模型,给出了积分和积分-微分方程,并当理赔量为指数分布时给出了破产概率的具体表达式.     

复合二项过程风险模型的精细大偏差及有限时间破产概率

讨论基于客户到来的复合二项过程风险模型.在该风险模型中,假设索赔额序列是独立同分布的重尾随机变量序列,不同保单发生实际索赔的概率可以不同,则在索赔额服从ERV的条件下,得到了损失过程的精细大偏差;进一步地,得到了有限时间破产概率的Lundberg极限结果.     

带干扰风险的破产模型的研究

本文对古典风险模型中保险公司按单位时间常数率收到保险费的假设做了改进,将每次收到的保险费的次数看作是复合泊松过程,将每次收到的保费和每次的理陪额均看作是服从指数分布的随机变量,并引入带干扰风险的扰动项,从而对古典风险模型进行推广,且给出了相应的破产概率上界,分析了破产概率的上界与准备金,索赔额,净保费和扰动方差之间的关系.     

The Perturbed Compound Poisson Risk Process with Investment and Debit Interest

In this paper, we study absolute ruin questions for the perturbed compound Poisson risk process with investment and debit interests by the expected discounted penalty function at absolute ruin, which provides a unified means of studying the joint distribution of the absolute ruin time, the surplus immediately prior to absolute ruin time and the deficit at absolute ruin time. We first consider the stochastic Dirichlet problem and from which we derive a system of integro-differential equations and the boundary conditions satisfied by the function. Second, we derive the integral equations and a defective renewal equation under some special cases, then based on the defective renewal equation we give two asymptotic results for the expected discounted penalty function when the initial surplus tends to infinity for the light-tailed claims and heavy-tailed claims, respectively. Finally, we investigate some explicit solutions and numerical results when claim sizes are exponentially distributed.     

Value at Ruin and Tail Value at Ruin of the Compound Poisson Process with Diffusion and Efficient Computational Methods

We analyze the insurer risk under the compound Poisson risk process perturbed by a Wiener process with infinite time horizon. In the first part of this article, we consider the capital required to have fixed probability of ruin as a measure of risk and then a coherent extension of it, analogous to the tail value at risk. We show how both measures of risk can be efficiently computed by the saddlepoint approximation. We also show how to compute the stabilities of these measures of risk with respect to variations of probability of ruin. In the second part of this article, we are interested in the computation of the probability of ruin due to claim and the probability of ruin due to oscillation. We suggest a computational method based on upper and lower bounds of the probability of ruin and we compare it to the saddlepoint and to the Fast Fourier transform methods. This alternative method can be used to evaluate the proposed measures of risk and their stabilities with heavy-tailed individual losses, where the saddlepoint approximation cannot be used. The numerical accuracy of all proposed methods is very high and therefore these measures of risk can be reliably used in actuarial risk analysis.     

Finite Time Ruin Probabilities and Large Deviations for Generalized Compound Binomial Risk Models

In this paper, we extend the classical compound binomial risk model to the case where the premium income process is based on a Poisson process, and is no longer a linear function. For this more realistic risk model, Lundberg type limiting results for the finite time ruin probabilities are derived. Asymptotic behavior of the tail probabilities of the claim surplus process is also investigated.     

复合二项风险模型下破产概率的Pollazek-Khinchin公式

本文考虑复合二项风险模型破产概率问题,首先通过研究Gerber-Shiu折现惩罚函数,运用概率论的分析方法得到了其所满足的瑕疵更新方程,再结合离散更新方程理论研究了其渐近性质,最后,运用概率母函数的方法得到了与经典的Gramer-Lundberg模型类似的破产概率Pollazek-Khinchin公式．     

复合二项风险模型下破产概率的Po11azek-Khinchin公式

本文考虑复合二项风险模型破产概率问题,首先通过研究Gerber-Shiu折现惩罚函数,运用概率论的分析方法得到了其所满足的瑕疵更新方程,再结合离散更新方程理论研究了其渐近性质,最后,运用概率母函数的方法得到了与经典的Gramér-Lundberg模型类似的破产概率Pollazek-Khinchin公式.     

带干扰广义Elang(n)风险过程的破产前最大盈余

本文考虑了索赔时间间距为广义Erlang(n)分布的带干扰更新(Sparre Andersen)风险过程.所用的方法类似于Albrecher,et al.(2005),即将广义Erlang(n)随机变量分解成n个独立的指数随机变量的和.建立了破产前最大盈余所满足的积分-微分方程,讨论了索赔量分布为K<,m>分布时的特殊情形.     

一类多险种风险过程的破产概率

由于保险公司风险经营规模的不断扩大,考虑到用单一险种的风险模型来描述风险经营过程的局限性,本文建立了多险种风险模型,并对其中一类特殊的风险模型的破概率进行了研究,给出了初始资本为0时破产概率Ψ（0）的明确表达式,以及初始资本为μ的破产概率Ψ（μ）的近似估计和在某些特殊情形下Ψ（μ）的明确表达式。