竞争型二元风险模型破产概率

本文研究了竞争型的二元风险模型,定义了两类破产概率以及状态过程,利用经典风险模型的已有结果和条件期望的性质,得到两类破产概率表达式,以及单个保险公司有限时间破产概率和最终破产概率,并给出两个保险公司的状态过程的概率分布列.     

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.     

一类相依索赔离散风险模型研究

研究了一类相依索赔的离散风险模型,得到了利率为0时模型的最终破产概率所满足的积分方程,以及破产持续n期的概率所满足的表达式.进而,得到了利率不为0时该模型的最终破产概率所满足的积分方程,并利用鞅论技巧导出了最终破产概率的一个Lundberg型上界,最后运用Matlab软件随机模拟破产概率并与Lundberg型上界作比较.     

常利率下的Cox模型的破产概率

讨论了常利率下的Cox模型的破产概率 ,分别得到了条件破产概率和最终破产概率所满足的积分方程 .     

常利率下带干扰的Cox模型的破产概率

讨论了常利率下带干扰的Cox模型的破产概率,分别得到了条件破产概率和最终破产概率所满足的微积分方程.     

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。     

寿险中的破产理论及应用

本文研究了求解寿险中破产概率的简洁方法 ,得到寿险破产模型 ,设计了求解寿险中的破产概率的一种算法 ,并得到寿险破产概率的一个上界。     

具有相依结构离散时间模型破产概率的上界

研究两类具有相依结构的离散时间风险模型的破产概率问题.其中,索赔和利率过程假设为2个不同的自回归移动平均模型.利用更新递归技巧,首先得到了该模型下破产概率所满足的递归方程.然后,根据该递归方程得到了破产概率的上界估计.最后对两类风险模型的破产概率的上界进行了比较.     

一类推广负风险和模型的破产概率

本文研究了带干扰的两险种负风险和模型的破产问题.利用无穷小方法,给出了该风险模型破产概率所满足的微分-积分方程,并推导出破产概率满足的Lundberg型不等式.最后指出了当索赔服从负指数分布时破产概率的上界,推广了经典风险模型的结果.     

马氏利率下相关险种的离散风险建模和破产概率

在随机利率服从有限齐次Markov链下,建立相关险种离散风险模型,采用递推方法得到了有限时间破产概率的递推等式和最终破产概率的积分等式;给出了有限时间破产概率和最终破产概率的上界,导出了破产时刻余额分布的计算等式.     

On the first time of ruin in the bivariate compound Poisson model

This paper considers a bivariate compound Poisson model for a book of two dependent classes of insurance business. We focus on the ruin probability that at least one class of business will get ruined. As expected, general explicit expressions for this bivariate ruin probability is very difficult to obtain. In view of this, we introduce the so-called bivariate compound binomial model which can be used to approximate the finite-time survival probability of the assumed model. We then study some simple bounds for the infinite-time ruin probability via the association properties of the bivariate compound Poisson model. We also investigate the impact of dependence on the infinite-time ruin probability by means of multivariate stochastic orders.     

The compound binomial risk model with time-correlated claims

In this paper, we consider the compound binomial risk model with the time-correlated claims. It is assumed that every main claim will produce a by-claim but the occurrence of the by-claim may be delayed. We obtain the recursive formula of the joint distribution of the surplus immediately prior to ruin and deficit at ruin. Furthermore, the ruin probability is given by means of ruin probability and the deficit at ruin of the classical compound binomial risk model. Finally, we derive an upper bound for the ruin probability.     

具有Vasicek利率的风险过程的破产概率的分解(英文)

In this paper, it is assumed that an insurer with a jump-diffusion risk process would invest its surplus in a bond market, and the interest structure of the bond market is assumed to follow the Vasicek interest model. This paper focuses on the studying of the ruin problems in the above compounded process. In this compounded risk model, ruin may be caused by a claim or oscillation. We decompose the ruin probability for the compounded risk process into two probabilities： the probability that ruin caused by a claim and the probability that ruin caused by oscillation. Integro-differential equations for these ruin probabilities are derived. When the claim sizes are exponentially distributed, the above-mentioned integro-differential equations can be reduced into a three-order partial differential equation.     

含投资因素的崩溃模型

本文讨论了已推广的保险公司的崩溃模型.本文得到了离散时间的崩溃模型复利情形下的崩溃概率公式,也得出了连续时间的崩溃模型崩溃概率的明确解和Vokterra积分方程.这些结果推广了经典崩溃模型中的相应结果.     

On the decomposition of the absolute ruin probability in a perturbed compound Poisson surplus process with debit interest

We consider a compound Poisson surplus process perturbed by diffusion with debit interest. When the surplus is below zero or the company is on deficit, the company is allowed to borrow money at a debit interest rate to continue its business as long as its debt is at a reasonable level. When the surplus of a company is below a certain critical level, the company is no longer profitable, we say that absolute ruin occurs at this situation. In this risk model, absolute ruin may be caused by a claim or by oscillation. Thus, the absolute ruin probability in the model is decomposed as the sum of two absolute ruin probabilities, where one is the probability that absolute ruin is caused by a claim and the other is the probability that absolute ruin is caused by oscillation. In this paper, we first give the integro-differential equations satisfied by the absolute ruin probabilities and then derive the defective renewal equations for the absolute ruin probabilities. Using these defective renewal equations, we derive the asymptotical forms of the absolute ruin probabilities when the distributions of claim sizes are heavy-tailed and light-tailed. Finally, we derive explicit expressions for the absolute ruin probabilities when claim sizes are exponentially distributed.     

Ruin problems for a discrete time risk model with random interest rate

In this paper, we study a discrete time risk model with random interest rate. The convergence of the discounted surplus process is proved by using martingale techniques, an expression of ruin probability is obtained, and bounds for ruin probability are included. In the second part of the paper, the distribution of surplus immediately after ruin, the distribution of surplus just before ruin, the joint distribution of the surplus immediately before and after ruin, and the distribution of ruin time are discussed.     

变利率风险模型下破产概率的渐近估计

本文考虑变利率的离散时间风险模型的破产概率．在个体净损失服从ERV族和DnL族时,分别得到了有限时间和无限时间破产概率的渐近估计及上下界表达式,并利用matlab软件对有限时间破产概率的下界进行了数值模拟．     

带干扰的常利率超额再保险Poisson风险模型的最优自留额

本文推广了Centeno[1],何树红[2],张茂军[3]的模型,研究带干扰的常利率超额再保险风险模型。首先用鞅方法求得其调节函数,进而证明Lundberg不等式,给出有限时间破产概率上界,并讨论最优自留额的确定。     

常利率下自回归索赔模型的破产概率的界

研究常利率下的一个广义连续时间更新风险模型的(最终)破产概率,其中自回归过程模拟相依的索赔过程.通过更新的递推方法,得到了此模型破产概率的指数上、下界.