【作者】 郎艳怀；

【导师】 冯恩民；

【作者基本信息】 大连理工大学 ， 运筹学与控制论， 2002， 博士

【摘要】 保险，作为商品社会中处理风险的一种有效方法，已被世界普遍采纳。在现代保险业的发展中，科学的理论方法，特别是精算理论起着十分重要的作用。我国现已加入WTO，但保险业与国际接轨还有很大的差距，迫切需要引进国际先进的保险精算理论，并结合我国实际加以运用。本文在保险精算理论及其应用方面作了较深入的研究，主要作了以下几个方面的工作。 1 保险精算综述 综述了保险精算学的起源及其发展简史，国际国内保险市场的现状与趋势；介绍了人寿保险精算理论的基本原理。 2 综合保险产品的险种设计 本文建立了综合人寿保险精算模型，把几种不同性质的保险产品统一于一个综合模型之中，其中包括了生存年金、终身寿险和还本部分。这个保险精算模型具有如下性质： (a)保险公司可以根据实际情况调整参数，不同参数的组合可以得到不同的保险产品，灵活适用性较强； (b)年金的引入，可以缓解投保人退休后的经济窘境，避免或减小因退休而面临的经济影响，保险的社会保障性得到了很好的体现； (c)模型中的还本部分，使得这种保险产品具有储蓄和保险的双重功能，不仅扩大了保险的社会职能，而且对于投保人来说，多了一种安全的投资选择； (d)年金连续的情况下，建立了具有储蓄功能的养老保险精算模型。 在此模型的基础上，建立了分式优化模型，对最优解的存在性进行了讨论，给出了最优解的存在性定理。 3 随机利率下的综合人寿保险模型 传统的精算理论中，都是假定利率是确定的，然而实际上利率具有随机性。寿险中的利率随机性是风险产生的重要因素。利率降低产生的风险，对于保险公司来说是致命的。为此，建立了随机利率下的综合人寿保险模型。随机利率的引进，降低了保险公司的风险程度，保险的公平性等原则得到了较好的体现。保险公司通过参数的组合选择，得到不同的随机利率下的保险产品；同时，建立了随机优化模型。4 基于对策理论的最优保险 将对策理论应用于保险实践中，投保过程可以由二人零和对策来描述，应用二人零和对策理论讨论模型中保险费的最优值存在性及如何得到保险费的最优解。保险公司运用此模型可以虚拟保险费的定价，进行市场调查，然后利用反馈的数据求得最优的保险费价格，推出最优的保险险种。对策论的应用，就公平合理地厘定保险费提供了科学的理论方法，保险公司和投保人在保险契约中可以同时拥有最优的选择。5 效用与保险最优决策 从投保人的角度考虑，应用效用函数讨论使投保人效用达到最优值的方案和方法。更多还原

【Abstract】 This dissertation is devoted to the study of insurance actuarial theory and its applications. The main works obtained in this dissertation are summarized as follows:1 Summarization of insurance actuarial theoriesReview the history of insurance actuarial science and its development and introduce its basic theories. Study the status and trend of international insurance market and that in our country.2 The aggregate model of life insuranceEstablish an aggregate model of life insurance by applying the alien modernly insurance actuarial theories and techniques, including deferred life annuities, whole life insurance and returnable premiums. The model has the following properties:(a) Through the regulation of various parameters in the model, various insurance products can be obtained;(b) The introduction of whole life annuities in the model eases economic predicament when the insured retire;(c) A returnable premium part in the model makes the insurance products have double functions of insurance and savings;(d) An endowment insurance actuarial model also can be gotten when annuity is continuous.And construct an optimization model based on aggregate model of life insurance.3 Aggregate model of life insurance with stochastic interestConstruct an aggregate model of life insurance with stochastic interest aiming at both the randomness of interest in practice and the importance of stochastic interest in life insurance. The introduction of stochastic interest in the model lessen risk of insurance company. The insurance company can also acquire various insurance products withstochastic interest by different combinations of parameters. Establish a stochastic optimization model based on aggregate model of life insurance with stochastic interest.4 The optimal insurance based on game theoryStudy the above aggregate model of life insurance by applying the game theories. The insurance process is characterized by the game of two-person zero-sum for the first time: The existence of the optimal value of premium in the model and how to obtain the optimal value are analyzed in detail based on the game theories. The game theory provides a new scientific method so as to determine an optimal premium between the insured and the insurance company. The insurance company can apply the model to dummy the premium, investigate market, obtain the optimal premium and determine the optimal insurance product accordingly.5 Utility and optimal game of insuranceApply the utility theory to insurance in order to confirm the optimal insurance premium for the insured.更多还原