【作者】 靳永山；

【导师】 边馥萍；

【作者基本信息】 天津大学 ， 运筹学与控制论， 2004， 硕士

【摘要】 保险业是经营风险的特殊金融服务行业。随着社会经济的发展和现代科学技术的广泛应用,一次事故可能造成的物质损失和人身伤亡的损失程度不断扩大,任何保险公司也不敢独自承担巨额的风险，保险监管部门也不允许这样做。为保持经营的稳定性，扩大业务规模，再保险成为必然的选择。再保险种基本问题是自留额的选择，即原保险人自留多少？分保多少的问题？理论上对自留额的确定利用效应函数来解决，然而效应函数是一种主观、因人而异并难以确定的。因此把效应方法用于实际再保险决策问题是难以操作的。 DEA 方法是评价具有相同类型投入和产出的若干生产与非生产部门 (简称决策单元) 相对效率的系统分析方法.广泛用于来评价生产活动的最优性.然而在现实的经济活动中,投入产出因素往往受到随机因素的干扰,由此而产生测量误差,数据噪声.同时经济现象本身也具有波动性及周期性,因此.决策单元的输入和输出往往不是确定的数值,而是服从一定随机分布的变量,因而应用确定性的 DEA模型[1]求解，具有较大的局限性. 本文在广泛查阅国内外文的基础上，对 DEA 理论、方法与应用进行了较深入地探讨，分析了基本的 DEA 模型，DEA 有效性理论以及 DEA 方法的基本思想，基于分治思想对随机 DMU 有效性的进行了分析，提出了一种新的随机 DMU问题的求解方法,主要讨论了输入输出均具有共同趋向的多输入多输出的随机DEA 问题的求解过程和算法。基于均值-方差原理讨论了随机 DMU 的相对稳定有效性。结合再保险的理论，将数据包络思想应用到再保险决策中，对再保险中再保险方案的选择、预测再保险的有效性进行了分析，具有较强的实用性。更多还原

【Abstract】 Insurance is a special finance trade of managing risk. As the development ofsociety and economy, technology and science are applied abroad, the degree of loss ofmatter and casualty enlarged in an accident. Any insurance dare not bear the risk ofmint and it is not allowed by wardship. To keep stability and enlarge the scale ofmanaging, reinsurance becomes the necessity choice, the basic problem of reinsuranceis to deal with premium and keep retention. In theory, it can be answered by utility.but utility function is subjective and can’t define easily, so to apply the means ofutility in practice of decision-making of reinsurance is difficulty. Data envelopment analysis (DEA) is a power technique of measuring the relativeefficiency of a set of decision-making units (DMUs) with the same inputs and outputs.This technique has been widely applied in measuring the optimal property, but in theactivity of economy, inputs and outputs is disturbed by error and fluctuate andperiodicity, so the stochastic data variations in inputs and outputs may be incorporatedinto the DEA framework for evaluating the efficiency. In this paper, the development of Data Envelopment Analysis (DEA) theories,DEA methods and DEA applications are discussed, the basic DEA model DEAefficiency theories are analyzed. Based on divided and conquer, the define ofevaluation of stochastic DMU from another aspect is presented and given a newmethod of solving, the process and algorithm of many input and output stochasticDMU provided with common trend is discussed in main. Based on principle ofmean-variance, this paper firstly advances this definition of the relative -stableefficiency of stochastic DMUS and presents the model DEA of the relative-stableefficiency measurement and analyses the relative-stable efficiency, and gives thecalculation of it. The idea of data envelopment analysis is applied intodecision-making of reinsurance, implying the choice project and the forecasting therelative efficiency of reinsurance and analyzing the feasibility of algorithm.更多还原