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1、The Continuous Liability Reserve Runds Based onUncertainty Interest RateMajor：StatisticDirection of Study：Uncertainty Theory and ActuarialGraduate Student： Wu ShuaiSupervisor：Prof. Lin LiangCollege of ScienceGuilin University of TechnologySeptember, 2012 to April, 2013IIIII摘要在精算实践过程中，准备金的提取起着举足轻重的作用
2、。学者们发现，当寿险保单责任期很长时，利率和死亡率在保险公司准备金提取方面起着关键性作用。精算学发展早期，由于大多数国家都为固定利率制，因此利率一直采用固定利率。但随着近年来世界爆发的金融危机和市场物价起伏不定，很多国家将利率调整作为国家宏观调控的重要手段，利率的影响变得越来越突出。近年来，学者们开始越来越多的关注这种影响带来的危机，并逐渐打了传统的固定利率假设，开始致力于研究可变利率下的寿险精算问题，他们通过将利率刻画为随机过程、模糊变量等，试图去量化这种不确定性的波动。刘宝碇教授为了更准确的描述生活中这种不确定性，建立了不确定理论，提出了不确定过程，并建立了不确定金融市场下的股价模型，为金
3、融数学的研究提供了一种新的理论基础。本文在广泛吸收国内外研究成果的基础上，将以刘宝碇教授的不确定理论的角度，研究在不确定金融市场下的完全连续型责任准备金。以不确定过程分析不确定环境下的保险利率，并在此基础上进一步研究不确定利率环境下的完全连续型终身寿险、定期寿险、定期支付终身寿险，以及延期生命年金的保费和责任准备金的计算公式，给出相应的实例进行计算，并对固定利率、随机利率和不确定利率下的责任准备金和保费进行比较分析。本文的主要创新点包括：1、在不确定环境下，假设利息力满足不确定过程，极大丰富了利率理论，为涉及利率的相关问题提供了新的途径和方法；2、通过不确定利息力，建立了寿险精算和生存年金的现
4、值公式，并得到全新的保费模型，为精算学开辟了新的道路和模式；3、基于不确定过程下的利息力假设和保费计算公式，得出保险公司计提责任准备金的计算方法；4、通过常见的四种保单形式，对固定利率、随机利率和不确定利率下的保费和责任准备金的数值进行对比分析，提出保险公司在计算保费和责任准备金时可供选择的贴切方法。关键词：不确定利率, Weiner-Poisson过程,不确定过程, Canonical过程。IVAbstractIn the process of actuarial practice, the extraction of reserve plays an importantrole. Scho
5、lars have found that when responsibility period is long, the life insurancepolicy rates and mortality play a key role in insurance companies provisioning. Whenthe actuarial science developed early, most countries used the fixed rate system. Butwith the outbreak of the financial crisis in the world ,
6、 the fluctuate of market prices,adjusting interest rates become aan important means of macroeconomic regulationand control the country, therefor，the influence of interest rate is becoming more andmore prominent. In recent years, scholars began to put more and more attention to theimpact the crisis,
7、and gradually made the traditional fixed rate hypothesis, studiedunder the variable rate of life insurance actuarial, they will through the interest rate asstochastic process, a fuzzy variable, etc., attempt to quantify the volatility of theuncertainty.Liu established the uncertainty theory, put for
8、ward uncertain process and theuncertain stock model in the case of financial markets, for the financial mathematicsresearch provides a new theoretical basis.In this paper, uncertain process was used to analyze the insurance rates , and wewill get the formula of liability reserve in continuous whole
9、life, term life insurance,whole life of paying regularly, as well as the extension of life annuity insurance .In this paper，the main innovations include:1. In an uncertain environment, we assume that the interest force meet uncertainprocess. This will enrich the theory of interest rate. As well as，i
10、t provides a new wayand method for the relevant matters.2. Based on the uncertain interest force, we will establish a life annuities and lifeinsurance actuarial present value formula,get a new premium model, and offer anew way for actuarial mode.V3. Under interest force hypothesis of uncertain proce
11、ss, the calculation formulaof premium and provision for liability insurance will be obtained.4. Through the four common forms of actuarial, the premium and liabilityreserve funds by fixed interest rate, stochastic interest rate and uncertain interest ratewill be compared and get some numerical analysis.Key words: Uncertainty Interest rate, Weiner-Poisson process, Uncertaintyprocess, Canonical process.VI目录摘要. IABSTRACT. III目录. VII主要符号对照表. VII第一章引言.11.1选题背景及意义. 11.2国内外研究动态.
