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.     

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.     

双相依结构下离散时间风险模型的破产概率渐近估计及数值模拟

本文研究了具有双相依结构及重尾索赔噪声项的离散时间风险模型的有限时间破产概率.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;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依.保险公司单期保费收入是恒定的常数,当单边线性过程的噪声项服从重尾分布时,本文得到离散时间风险模型有限时间破产概率的渐近估计.最后利用蒙特卡罗模拟方法验证所得结果.     

考虑一般投资收益和时间相依索赔情形下二维带扰动风险模型的有限时间破产概率渐近估计

考虑具有一般投资收益过程的二维带扰动保险风险模型,假定保险公司盈余的投资收益过程由右连左极随机过程刻画,且两种索赔额与索赔到达时间间隔服从S armanov相依结构.当索赔额分布属于正则变化尾分布族时,得到有限时间破产概率的渐近公式.当描述投资收益过程的右连左极过程分别取Lévy过程,Vasicek利率模型,Cox-Ingersoll-Ross(CIR)利率模型,Heston模型时,得到相应投资收益情形下破产概率的渐近公式.     

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.     

负相依索赔下基于进入过程风险模型的破产概率

提出了一个基于客户到来的泊松过程风险模型,其中不同保单发生实际索赔的概率不同,假设潜在索赔额序列为负相依同分布的重尾随机变量序列,且属于重尾族L∩D族的条件下,得到了有限时间破产概率的渐近表达式.     

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.     

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.     

一类带投资和副索赔的二维时依风险模型破产概率的渐近估计

考虑一类二维风险模型,其中两个保险公司共同承担所有的索赔,且每个(主)索赔都会引起一个副索赔.假定两个保险公司均将其资产投资到金融市场中,其投资回报服从几何Levy过程.在索赔分布属于C族以及索赔额与索赔到达时间间隔具有某种相依结构的条件下,对该二维风险模型盈余过程的有限时破产概率进行渐近估计.     

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.     

Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model

Consider an insurer who is allowed to make risk-free and risky investments. The price process of the investment portfolio is described as a geometric Lévy process. We study the tail probability of the stochastic present value of future aggregate claims. When the claim-size distribution is of Pareto type, we obtain a simple asymptotic formula which holds uniformly for all time horizons. The same asymptotic formula holds for the finite-time and infinite-time ruin probabilities. Restricting our attention to the so-called constant investment strategy, we show how the insurer adjusts his investment portfolio to maximize the expected terminal wealth subject to a constraint on the ruin probability.     

Asymptotics in a time-dependent renewal risk model with stochastic return

In this paper we study the asymptotic tail behavior for a non-standard renewal risk model with a dependence structure and stochastic return. An insurance company is allowed to invest in financial assets such as risk-free bonds and risky stocks, and the price process of its portfolio is described by a geometric Lévy process. By restricting the claim-size distribution to the class of extended regular variation (ERV) and imposing a constraint on the Lévy process in terms of its Laplace exponent, we obtain for the tail probability of the stochastic present value of aggregate claims a precise asymptotic formula, which holds uniformly for all time horizons. We further prove that the corresponding ruin probability also satisfies the same asymptotic formula.     

Asymptotic formula for a partition function of reversible coagulation-fragmentation processes

We construct a probability model seemingly unrelated to the considered stochastic process of coagulation and fragmentation. By proving for this model the local limit theorem, we establish the asymptotic formula for the partition function of the equilibrium measure for a wide class of parameter functions of the process. This formula proves the conjecture stated in [5] for the above class of processes. The method used goes back to A. Khintchine.     

Ruin probability of the renewal model with risky investment and large claims

The ruin probability of the renewal risk model with investment strategy for a capital market index is investigated in this paper. For claim sizes with common distribution of extended regular variation, we study the asymptotic behaviour of the ruin probability. As a corollary, we establish a simple asymptotic formula for the ruin probability for the case of Pareto-like claims. This work was supported by National Natural Science Foundation of China (Grant Nos. 10571167, 70501028), the Beijing Sustentation Fund for Elitist (Grant No. 20071D1600800421), the National Social Science Foundation of China (Grant No. 05&ZD008) and the Research Grant of Renmin University of China (Grant No. 08XNA001)     

Ruin probability in the presence of interest earnings and tax payments

In this paper we investigate the ruin probability in a general risk model driven by a compound Poisson process. We derive a formula for the ruin probability from which the Albrecher–Hipp tax identity follows as a corollary. Then we study, as an important special case, the classical risk model with a constant force of interest and loss-carried-forward tax payments. For this case we derive an exact formula for the ruin probability when the claims are exponential and an explicit asymptotic formula when the claims are subexponential.     

经典风险模型中破产概率的一个渐近式

本文研究经典风险模型中破产概率的渐近行为．利用几何和的方法，获得了索赔额的分布属于S（γ）．γ〉0。时破产概率的一个局部渐近式．同时．给出了一个具体的数值的例子．     

Equiaffine inner parallel curves of a plane convex body and the convex hulls of randomly chosen points

Summary. A general formula is proved, which relates the equiaffine inner parallel curves of a plane convex body and the probability that the convex hull of j independent random points is disjoint from the convex hull of k further independent random points. This formula is applied to improve some well-known results in geometric probability. For example, an estimate, which was established for a special case by L. C. G. Rogers, is obtained with the best possible bound, and an asymptotic formula due to A. Rényi and R.␣Sulanke is extended to an asymptotic expansion. Received: 21 May 1996     

Random ℓ‐colourable structures with a pregeometry

We study finite ℓ‐colourable structures with an underlying pregeometry. The probability measure that is used corresponds to a process of generating such structures by which colours are first randomly assigned to all 1‐dimensional subspaces and then relationships are assigned in such a way that the colouring conditions are satisfied but apart from this in a random way. We can then ask what the probability is that the resulting structure, where we now forget the specific colouring of the generating process, has a given property. With this measure we get the following results: (1) A zero‐one law. (2) The set of sentences with asymptotic probability 1 has an explicit axiomatisation which is presented. (3) There is a formula (not directly speaking about colours) such that, with asymptotic probability 1, the relation “there is an ℓ‐colouring which assigns the same colour to x and y ” is defined by . (4) With asymptotic probability 1, an ℓ‐colourable structure has a unique ℓ‐colouring (up to permutation of the colours).     

Ruin probability in a one-sided linear model with constant interest rate

This paper investigates the ruin probability of a generalized renewal model with a constant interest rate, in which a one-sided linear model is used for the dependent claim process. An explicit asymptotic formula and an exponential upper bound are obtained for the ruin probability.