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.     

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.     

带马氏利率的离散时间风险模型的破产概率

本文考虑一类保费和理赔额均为随机变量,且利率为马氏链的离散时间风险模型。推出了有限时间和最终时间破产概率的递归方程,并用归纳法得到了最终时间破产概率的上界表达式。     

利率为马氏链的离散时间风险模型的破产概率(英文)

本文考虑了带随机利率的离散时间风险模型.在假设利率为马氏链条件下,得到了有限时间和最终破产概率所满足的递推积分方程,以及最终破产概率的Lundberg不等式.     

保费收取过程是随机过程的双险种风险模型

研究保费收取过程是一个随机过程的双险种风险模型,得出了Lundberg上界、最终破产概率、不破产所满足的微积分方程、索赔服从指数分布的不破产概率、有限时间不破产所满足的微积分方程.     

离散时间的双Poisson模型的破产概率

本文在离散复合Poisson风险模型的基础上,研究保费的收取也为一个Poisson过程的模型, 在保费收取量和理赔量都离散取整数值时,我们运用转移概率推导出了保险公司在有限时间内破产的概率以及最终破产概率的级数表达式和矩阵表达式.     

容忍最小收益下变保费率的更新风险模型

经典的风险模型在研究破产概率时,定义的破产时刻为盈余过程首次取负值的时刻,而讨论低于某一限度时的时刻为破产时刻更有实际的意义.本文将这一限度定义为容忍最小收益,首先讨论了容忍最小收益下变保费率的更新风险模型最终的破产概率;并进一步讨论了它在大索赔情形下有限时间内的破产概率的性质.     

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)。     

随机利率及保费的离散风险模型中的破产问题

本文研究了利率、保费均为随机变量的两个离散风险模型.利用递推的方法,得到了有限时间内的破产概率和最终破产概率所满足的积分方程,以及盈余首次穿过给定水平时刻的分布的递推公式,从而可以对保险公司各个破产指标得出数值结论.     

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．     

Control of ruin probabilities by discrete-time investments

The control problem of controlling ruin probabilities by investments in a financial market is studied. The insurance business is described by the usual Cramer-Lundberg-type model and the risk driver of the financial market is a compound Poisson process. Conditions for investments to be profitable are derived by means of discrete-time dynamic programming. Moreover Lundberg bounds are established for the controlled model.     

Exponential Bounds for Ruin Probability in Two Moving Average Risk Models with Constant Interest Rate

The authors consider two discrete-time insurance risk models. Two moving average risk models are introduced to model the surplus process, and the probabilities of ruin are examined in models with a constant interest force. Exponential bounds for ruin probabilities of an infinite time horizon are derived by the martingale method.     

一类相依两险种风险模型的分类破产概率

本文考虑文[1]中引入的一类索赔达到计数过程相关的两险种风险模型.利用更新方法,获得了该风险模型的分类破产概率的渐进结果,并给出了指数索赔情形下分类破产概率的表达式,从而改进了文[1]中的相关结果.     

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.     

一类基于进入过程保险风险模型的破产概率(英文)

In this note,one kind of insurance risk models with the policies having multiple validity times are investigated.Explicit expressions for the ruin probabilities are obtained by using the martingale method.As a consequence,the obtained probability serves as an upper bound for the ruin probability of a newly developed entrance processes based risk model.     

多险种复合Poisson风险模型和破产概率

经典风险模型只描述了单一险种的经营模式,具有局限性,本文对多险种的复合Poisson风险模型的破产概率进行了研究。本文给出了初始资本为0时破产概率皿（O）的明确表达式,以及理赔量服从指数分布且初始资本为u时破产概率ψ（u）的明确表达式。     

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??The paper considers a risk model with two dependent classes of
insurance business. In this model, the two claim number processes are partly sparsely
correlated through an Erlang(2) process. By introducing an auxiliary model, we obtain the
integral equations for ultimate ruin probabilities, and discuss the asymptotic property of
ruin probabilities by renewal approach. We also get the linear differential equations of
ruin probabilities of the model and the corresponding auxiliary model when claims follow
the exponential distributions, and show how solves the linear differential equations by a
specific example.     

宽象限相依随机变量部分和的中偏差及其在保险中的应用

研究了控制变换尾分布的宽象限相依实值随机变量部分和的中偏差.相应于所得到的理论结果,进一步给出了在相依保险风险模型中的两个应用;一是在基于顾客到达过程的保险风险模型中,保险公司盈余的渐近估计;二是在复合更新风险模型中,有限时和无限时破产概率的一致渐近估计.     

Ruin probabilities for an insurance company based on some stochastic risk models

The paper is concerned with a stochastic risk model with independent random claims and premiums. Recurrence formulas for the ruin probabilities of an insurance company at times of claim payments are obtained. Both the random premiums and the insurance damages are assumed to be independent and identically distributed. The number of claims and premiums are independent Poisson processes, both of which are independent of the size of premiums and claims. We consider the case when the random premiums and insurance damages are exponentially distributed and the more general case when they are gamma distributed with integer parameters. Based on the probabilities obtained in this paper, it is possible to calculate the ruin probabilities on infinite and finite time intervals. Examples are given.