第四章给出了破产概率的上下界。
In the fourth chapter, we derive some bounds of the ruin probabilities.
应用鞅论的方法，得出破产概率的一个不等式。
By using the method of Martingale, we get the inequality for the ultimately ruin probability.
用鞅方法得到了最终破产概率的上界及其具体表达式。
Using martingale approaches to obtain the upper bound of the ruin probability and it's expression.
在模型中考虑了利率、保费和理赔相依情形对破产概率的影响。
The effects of interest and the dependent situation of both the aggregate claims and the aggregate premiums on the ruin probabilities in the models are considered.
通过构造鞅的方法我们得到了无限时间下的破产概率的指数型上界。
Exponential bounds for ruin probabilities of an infinite time horizon are derived by martingale method.
在第四章，我们进一步把上一章的结果推广到无限时间破产概率的场合。
In Chapter 4 we further extend the result to the case of infinite time ruin probability with heavy tails.
本文的第二章得到了多重延迟更新风险模型中的破产概率的渐近表达式。
Chapter 2 delivers asymptotic forms for ruin probabilities in the multi-delayed renewal risk model with large claims as well as light tails.
讨论了赢余过程的性质，利用赢余过程的性质，给出了有关破产概率的两个结论。
The properties of surplus process are discussed and two conclusions related to the relevant bankruptcy probability are given by using the properties.
在保费收入可以改变的条件下，利用下鞅的收敛性，得到了破产概率的一个上界。
Under the condition of changing premium, the upbound of ruin probability was obtained by sub-martingale property.
对第三类风险模型进行研究，得到了有限时间破产概率和终极时间破产概率的上界估计。
At last we obtain the supremum estimation of the finite time ruin probability and the infinite time ruin probability in the third new risk model.
而破产概率的估计对于保险公司的稳定经营有着重要的作用，因此建立更符合实际的破产模型很有必要。
Because the estimate of ruin probability is important to stability of insurance company, so it is necessary to construct models which can describe realism well.
利用更新理论和随机过程等方法，给出了模型生存概率所满足的微积分方程关系式和破产概率的一个上界估计。
The differential and integral equation for survival probability and a upper bound of ruin probability are given by using renewal theory and stochastic process approach.
根据逐段决定马尔可夫过程具有马氏性和强马氏性，本文推导出了在古典风险模型下绝对破产概率的一个明确表达式。
In this paper, we deduced the explicit expression of the absolute ruin probability for classical risk model by using of the Markov property and strong Markov property of PDMP.
对一种离散风险模型的破产概率进行研究，并在理赔额分布函数已知的情况下推导出了破产概率的更易于计算的表达式。
The paper discusses the ruin probability of discrete risk mode and works out the expressing pattern easier for calculating ruin probability with the claim amount distribution function known.
在保险风险和金融风险为重尾分布的条件下，得到了二维风险模型两种破产概率的精确估计以及另外一个破产概率的上下界。
Some precise estimates were made of two kinds of ruin probabilities of finite time with heavy- tailed insurance risk and financial risk.
笔者将利率和退保因素引入寿险风险模型，得到了在死亡随机事件和撤出随机事件两种损失环境下，寿险破产概率的一个递推公式。
This paper introduces these two factors, thus works out a recursive formula of ruin probability under double-losses condition resulting from death and surrender.
本文研究两类一般的离散时间风险模型下的破产概率。即是在经典风险模型下考虑保费支付的不同时刻和利息的引入对破产概率的影响。
We consider two general classical risk model in this paper, the effects of timing of payments and interest on the surplus process can be included.
Kantrowitz说：“你死于癌症或车祸的概率都要比用破产摆脱助学贷款的可能性要高一点。”
"You're more likely to die of cancer orin a car crash than you are to get your loans discharged in bankruptcy," says Kantrowitz.
本文引入了一个含稀疏相关结构的二维风险模型，并基于此模型定义了三类不同的破产概率。
In this paper, we propose a two-dimensional risk model with thinning dependent structure and three different types of ruin probabilities are defined.
企业具有破产概率对企业的内在价值有直接影响。
Enterprise with bankruptcy probability has effected on its internal value.
本文首先利用随机时刻变换推广了一类带干扰的风险模型，然后讨论这类风险模型的条件破产概率。
This paper intends to extend risk model with disturbance by using random time transformation firstly, and then study the conditional ruin probability of the risk model.
然而，在实际生活中，利息是破产概率风险模型中非常重要的一个组成部分。
But interest is the important part in ruin probability of risk model in real life.
考察了有利息力风险模型的有限时间破产概率问题。
The finite time ruin probability of the risk model with constant interest force was considered.
考虑了复合负二项风险模型下的破产概率。
The ruin probability of compound negative binomial risk model is considered.
研究了常数利息力度下的破产概率。
This paper considered the ruin probability with constant interest force.
对一类带干扰的风险模型进行推广，并针对此模型给出了相应的破产概率上界。
Improvement of a risk model with interference is discussed and corresponding ruin probability upper bound is given for this model.
第三章讨论常利率下一类大额索赔离散风险模型的破产概率估计。
Chapter Three investigates the ruin probability of a discrete time risk model under constant interest rate with heavy tails.
第三章讨论常利率下一类大额索赔离散风险模型的破产概率估计。
Chapter Three investigates the ruin probability of a discrete time risk model under constant interest rate with heavy tails.
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