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  actuarial mathematics
Necessary and sufficient conditions of existence and uniqueness of solutions to integral equations of actuarial mathematics
      
A central problem of actuarial mathematics, i.e., the problem of pricing options (documents of a certain form that grant rights to buy or sell securities in the future), is considered.
      
The supermodular order on multivariate distributions has many applications in financial and actuarial mathematics.
      
The object of this paper is to demonstrate some features of the deterministic model of actuarial mathematics and to show its limit and range by viewing it in the framework of the stochastic model.
      
The present paper provides a unifying survey of Bayesian models in different areas of actuarial mathematics.
      
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Basing on the historical development of actuarial mathematics, this paper gives a survey of the three mathematical models in the researches for personal insurance by means of life insurance as a representative,and describes the present situation and future of the model researches. This is a reference for actuaries.

本文以保险数学的历史发展为背景,以生命保险为代表,论述了人身保险研究的三种数学模型,分析了模型研究和开发的现状,可以为我国人身保险系统模型的建立提供参考。

Life insurance system is a mechanism for reducing the financial impact of fhe random events of untimelydeath. Based on the historical development of actuarial mathematics, this paper gives a survey of the follow-ing three mathematical models in the researches for life insurance system: (a) the classical deterministic mod-el, (b) the risk model, (c) the probabilistic model. Moreover, the present situation and the future of themodel researches are described in this paper. These models will play a major role...

Life insurance system is a mechanism for reducing the financial impact of fhe random events of untimelydeath. Based on the historical development of actuarial mathematics, this paper gives a survey of the follow-ing three mathematical models in the researches for life insurance system: (a) the classical deterministic mod-el, (b) the risk model, (c) the probabilistic model. Moreover, the present situation and the future of themodel researches are described in this paper. These models will play a major role in Chinese life insurance sys-tem operations.

人寿保险系统是一种特定的经济机制,它对生命偶然事件发生所致的损失可得以减免。本文以保险统计数学的发展历史为背景,依层次地论述了寿险系统研究的三类数学模型:(1)古典确定性模型;(2)风险性模型;(3)概率性模型。同时分析了模型研究和开发的现状。这些模型在中国寿险经营运作中将起重要作用,并可为中国寿险建模提供参考。

Risk theory, as a part of insurance-or actuarial-mathematics, deals with stochastic models of an insurance business and studies the probability of ruin. The classical compound Poisson risk model is one of principal models. In such a model, the company receives a certain numbers of policies, which every policy has the same premiums,but in fact,the numbers of policy that the company received during the different unit time are different. Based on this fact,the classical compound Poisson risk model to...

Risk theory, as a part of insurance-or actuarial-mathematics, deals with stochastic models of an insurance business and studies the probability of ruin. The classical compound Poisson risk model is one of principal models. In such a model, the company receives a certain numbers of policies, which every policy has the same premiums,but in fact,the numbers of policy that the company received during the different unit time are different. Based on this fact,the classical compound Poisson risk model to a new risk model are generalized, which the arrival of term policies is a Poisson process. Then the Lundberg inequality and the formula for the ruin probability in this new model through stochastic process and martingale theory are concluded. Finally, the formula for the ruin probability is got in case of exponential claim amounts.

风险理论作为保险精算数学的一部分 ,主要处理保险事务中的随机风险模型并研究破产概率等问题。经典复合Poisson风险模型是主要的研究对象之一。在此模型下 ,保险公司按照单位时间常数速率收取保单 ,假定每张保单的保费相同。但在实际中 ,不同单位时间所收取的保单数常常不一样 ,是一个随机变量 ,可能服从某一离散分布。根据这一实际情况 ,将经典的复合Poisson风险模型进行了推广 ,将保单收入过程推广为一个参数为α >0的Poisson过程 ,并假定它与理赔过程独立 ,然后运用随机过程和鞅论的方法得出了推广后的Poisson模型的破产概率满足的Lundberg不等式和一般公式。最后得出了当个体索赔服从指数分布时破产概率的具体表达式。

 
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