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.     

Ruin Probabilities for Large Claims in Delayed Renewal Risk Model

This paper investigates ruin probabilities (x) in the delayed renewal risk model, where x is the initial capital of an insurance company. Under the assumption that the claim size is heavy-tailed, we aim at a tail equivalence relationship of (x) as x . The result we obtain in this paper is surprisingly the same as the previous classical results.This work was supported by National Science Foundation of China (No. 10071081).     

Discounted Aggregate Claim Costs Until Ruin in the Discrete-Time Renewal Risk Model

In this paper, we focus on analyzing the relationship between the discounted aggregate claim costs until ruin and ruin-related quantities including the time of ruin. To facilitate the evaluation of quantities of our interest as an approximation to the ones in the continuous case, discrete-time renewal risk model with certain dependent structure between interclaim times and claim amounts is considered. Furthermore, to provide explicit expressions for various moment-based joint probabilities, a fairly general class of distributions, namely the discrete Coxian distribution, is used for the interclaim times. Also, we assume a combination of geometrics claim size with arbitrary interlciam time distribution to derive a nice expression for the Gerber-Shiu type function involving the discounted aggregate claims until ruin. Consequently, the results are applied to evaluate some interesting quantities including the covariance between the discounted aggregate claim costs until ruin and the discounted claim causing ruin given that ruin occurs.     

Asymptotic Results for Ruin Probability of a Two-Dimensional Renewal Risk Model

In this article, some asymptotic formulas of the finite-time ruin probability for a two-dimensional renewal risk model are obtained. In the model, the distributions of two claim amounts belong to the intersection of the long-tailed distributions class and the dominated varying distributions class and the claim arrival-times are extended negatively dependence structures. Assumption that the claim arrivals of two classes are governed by a common renewal counting process. The asymptotic formulas hold uniformly for t ∈ [f(x), ∞), where f(x) is an infinitely increasing function.     

带利率和常数红利边界的对偶风险模型的研究

考虑带利率和常数红利边界的对偶风险模型.首先,给出破产为止总红利现值的期望满足的积分-微分方程,并且在指数收益下得到其封闭解.其次,推导出总红利现值的矩满足的积分-微分方程,在指数收益下给出其封闭解.最后,给出在特殊情形下的数值计算.     

Second Order Asymptotics for Infinite-Time Ruin Probability in a Compound Renewal Risk Model

Consider a compound renewal risk model, in which a single accident may cause more than one claim. Under the condition that the common distribution of the individual claims is second order subexponential, we establish a second order asymptotic formula for the infinite-time ruin probability. Compared with the traditional ones, our second order asymptotic result is more precise and effective, which can be demonstrated by the numerical studies.

     

具有常红利边界和延迟索赔的一类离散更新风险模型

考虑了具有常红利边界和延迟索赔的一类离散更新风险模型,其中间隔索赔到达时间从离散phase-type分布.定义了两种类型的索赔:主索赔和副索赔,主索赔以一定的概率引起副索赔且副索赔会以一定的概率被延迟到下一时段.通过引入辅助风险模型,推导了破产前红利折现期望满足的差分方程及其解.最后给出了当索赔额服从几何分布时的有关数值例子.     

常利率和门限分红策略下带干扰的泊松风险模型的绝对破产问题

本文考虑常利率和门限分红策略下带干扰的泊松风险模型的绝对破产问题,得到了累积分红现值的矩母函数, n阶原点矩所满足的积分-微分方程及边界条件;进一步得到了此模型下Gerber-Shiu折现罚函数所满足的积分-微分方程及相应边界条件,相应地将其转化为Volterra型积分方程,最后给出了索赔额为指数分布时绝对破产概率的解析表达式.     

更新风险模型破产赤字概率的上界

本文给出了更新风险模型破产赤字上界的一种算法,这种算法通过引入一个单调积分算子,得到了比Cramer-Lundberg上界更好的一些结果。     

常利息力下非标准连续时间更新风险模型破产概率的渐近性态

讨论一个非标准连续时间更新风险模型,其中理赔变量序列为一列两两尾拟渐近独立(TQAI)非负随机变量,在常数利息力假定下,得到了其有限时间破产概率的渐近估计式,并进一步讨论了估计的一致性,推广了[1,2,8]等文献的结果.     

双二项风险模型的破产概率

首先将经典的复合二项风险模型推广到保费到达过程与个体索赔过程是两个相互独立的二项过程的一种新模型，然后运用两种方法得出破产概率满足的一般公式和Lundberg不等式．     

竞争型的n元风险模型

保险市场中存在激烈的竞争,针对这种情形提出竞争型的n元风险模型,定义了两种破产时间,利用经典风险模型已有结论和条件期望的性质,得到相应的有限时间破产概率和最终破产概率表达式,以及每个保险公司有限时间破产概率和最终破产概率.     

常利息力影响下跳扩散模型的分红问题

本文中用常值利率驱动下的经典跳扩散模型模拟保险公司的盈余过程,研究了该模型在带壁分红策略下的若干问题.首先得出破产前分红折现的高阶矩所满足的积分微分方程,并在指数分布的情况下借助合流超几何函数给出了方程的显式解.其次关于破产前聚合分红得到了一些令人满意的结果,这些结果甚至对一般的分布都成立,另外讨论了分红流的次数和额度.最后研究了指数分布时破产赤字折现期望问题.本文的部分结论深化了精算学中一些已有研究成果.     

广义复合二项风险模型下的破产概率

将复合二项风险模型的保费收入推广为在单位时间内收取的保单数服从强度为α的poisson分布，利用鞅方法得出了其破产概率的一般公式及满足Lundberg不等式。     

On the Ruin Problem in a Markov-Modulated Risk Model

In this paper, we consider the compound Poisson risk model influenced by an external Markovian environment process, i.e. Markov-modulated compound Poisson model. The explicit Laplace transforms of Gerber–Shiu functions are obtained, while the explicit Gerber–Shiu functions are derived for the K _n -family claim size distributions in the two-states case.      

变破产下限风险模型的破产概率

近年来,很多文献对经典风险模型作了研究,并得出许多有用的结论。一般文献都是假定保险公司的破产下限为零,但在实际的保险实务中,当保险公司的盈余低于某一限度时,保险公司就要调整政策或宣布破产。本文研究了经典风险模型在假定变破产下限下的破产概率,得出了破产概率所满足的不等式,而且研究了当破产下限f(t)为某些特殊函数时,破产概率所满足的不等式或破产概率的具体表达式。最后本文给出了在推广后的风险模型中变破产下限破产概率所满足的不等式。     

Ruin Probabilities under a Markovian Risk Model

In this paper, a Markovian risk model is developed, in which the occurrence of the claims is described by a point process {N(t)}t≥0 with N(t) being the number of jumps of a Markov chain during the interval [0, t]. For the model, the explicit form of the ruin probability ψ(0) and the bound for the convergence rate of the ruin probability ψ(u) are given by using the generalized renewal technique developed in this paper.Finally, we prove that the ruin probability ψ(u) is a linear combination of some negative exponential functions in a special case when the claims are exponentially distributed and the Markov chain has an intensity matrix(qij)i,j∈E such that qm = qml and qi=qi(i 1), 1≤i≤m-1.     

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.     

带阈限分红策略的一类更新风险模型

本文考虑了索赔时间间距为Erlang(n)分布带阈限分红策略的更新风险模型的平均折现罚函数,建立了该函数所满足的积分-微分方程及更新方程,最后讨论了更新方程的解.