双到达过程带索赔成本风险模型的破产概率

本文考虑了一种双到达过程带索赔成本的一般更新过程的风险模型,主要是运用鞅来估计该模型在初始准备资金为U0的条件下有限时间内的破产概率ψ(U0,t)的最小上界和最终破产概率ψ(U0)。     

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).     

初论一类风险模型下的破产时刻罚金折现期望

考虑一类具有Poisson过程和Erlang(n)过程的风险模型的破产问题,该模型中保险公司具有两类保险,每类保险的理赔次数过程都是Poisson过程与一个共同的Erlang(n)过程的和.针对这类理赔相关的风险模型,就利息力为常数的情形得到破产时刻罚金折现期望的积分—微分方程.     

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.     

保费随机的离散风险模型的罚金期望函数

本文把经典的复合二项风险模型进行推广,其中保费收取方式不再是时间的线性函数而是一个二项过程.我们把它的罚金期望看成初始资本的函数,得到了罚金期望函数的递推公式和渐近估计,最后利用罚金期望函数的递推公式和渐近估计给出了几个重要的破产量的递推公式及其渐近估计.     

关于一类带常利率的更新风险模型的破产时值

该文研究了一类带利率的更新风险模型, 给出了Gerber-Shiu折现罚金函数所满足的积分方程, 并用无穷级数给出了其解的精确表达式; 推广了 Gerber-Shiu公式(见文献[4]); 最后利用递推技巧给出了破产概率的指数型上界.     

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.

     

复合Poisson-geometric风险模型下第n次索赔时的破产概率研究

在复合Poisson-geometric风险模型下,通过构造一个特殊的Gerber-Shiu函数,推导出此风险模型下Gerber-Shiu函数满足的更新方程,破产时刻和直到破产时的索赔次数的联合密度函数,得到了第n次索赔时的破产概率的数学表达式．     

索赔额是指数分布的马氏风险模型的破产概率

本文研究了马氏风险模型的破产概率,在索赔额服从指数分布或混合指数分布情形,通过解破产概率所满足的微积方程组,给出了破产概率的解析表达式.     

Ruin Probabilities for Risk Models with Ordered Claim Arrivals

Recently, Lefèvre and Picard (Insur Math Econ 49:512–519, 2011) revisited a non-standard risk model defined on a fixed time interval [0,t]. The key assumption is that, if n claims occur during [0,t], their arrival times are distributed as the order statistics of n i.i.d. random variables with distribution function F _t (s), 0?≤?s?≤?t. The present paper is concerned with two particular cases of that model, namely when F _t (s) is of linear form (as for a (mixed) Poisson process), or of exponential form (as for a linear birth process with immigration or a linear death-counting process). Our main purpose is to obtain, in these cases, an expression for the non-ruin probabilities over [0,t]. This is done by exploiting properties of an underlying family of Appell polynomials. The ultimate non-ruin probabilities are then derived as a limit.     

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.     

随机保费风险模型下的平均折现罚金函数

本文研究随机保费风险模型下与破产时刻相关的平均折现罚金函数. 与经典的Cram\'{e}r-Lundberg模型相比这里的保费过程不再是时间的线性函数, 而是一个与理赔独立的复合Possion过程. 我们得到了罚金函数所满足的积分方程, 它提供了一种研究破产量的统一方法. 利用该积分方程我们得到了破产时刻, 破产时赤字, 破产前瞬时盈余的Laplace变换; 并在指数分布的特殊情况下求出了他们的显著表达式, 推广了Boikov (2003)的结论.     

The Asymptotic Estimate of Absolute Ruin Probabilities in the Renewal Risk Model with Constant Force of Interest

In this paper, absolute ruin problems for a kind of renewal risk model with constant interest force are studied. For certain situations of the claim distribution with heavy tail, consider the surplus of the arrival time, and discrete the surplus process, then use the method of renewal function and convolution, we present the asymptotic properties of absolute ruin probability when the initial surplus tends to infinity.     

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本文给出了带随机重延迟的大额索赔更新风险模型的局部破产概率的渐近表达式, 它与 原更新风险模型相应的局部破产概率的渐近表达式一致     

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．     

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。