认证杯数学建模竞赛获奖论文

第七届“认证杯”数学中国

数学建模网络挑战赛

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我们的参赛队号为：2900

参赛队员(签名) ：

队员1：张安成

队员2：勾旭东

队员3：郑子嫣

参赛队教练员(签名)：李石涛

参赛队伍组别：本科组

第七届“认证杯”数学中国

数学建模网络挑战赛

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参赛队伍的参赛队号：（请各个参赛队提前填写好）：2900 竞赛统一编号（由竞赛组委会送至评委团前编号）：

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2014年第七届“认证杯”数学中国

数学建模网络挑战赛第一阶段论文题目土地储备方案的风险评估

关键词土地储备主成分分析层次分析法风险函数风险评估

摘要：

本文针对土地在收储过程中存在一定的金融风险这一问题，综合运用了单一变量分析、多元统计等方法，建立了主成分分析模型和层次分析法模型，利用EXCEL和MATLAB 软件及C语言程序进行求解，进而构造了土地储备方案的风险函数，并利用该风险函数，分别对附件二中给出的数据进行统计分析，从而找出10个风险最大的项目，并给出了造成这 10个项目风险较大的原因。

首先，我们分析了单一变量对土地储备方案的风险的影响。我们利用EXCEL软件，分别绘制了74组方案当中的收购储备面积、动态回收周期、总收储成本、预期收益的对比图，粗略的得出与土地储备方案风险有关的主要因素，即收购储备面积，总收储成本以及预期收益。得出影响风险的主要因素后，我们继续利用EXCEL软件，计算得出单位储备面积的成本以及收益，进而绘制出单位储备面积内，收益与成本的对比图，得出74组方案的收益与成本的差值范围。

其次，我们建立主成分分析模型，利用MATLAB软件进行相关系数的计算，相对准确的找出与土地储备方案的风险有关的主要因素，并构造了土地储备方案的风险函数，即

S=0.264X1+0.422X2-0.313X3

其中，S表示加权之和，即风险总值，X1表示收购储备面积，X2表示总收储成本，X3表示预期收益。

随后，我们根据构造的土地储备方案的风险函数S=0.264X1+0.422X2-0.313X3，将74组方案当中的相关数据代入，得出74组风险函数值，我们将74组数据值输入到C 语言程序中，设计从大到小顺序排列的程序，得出前10名的数据，与之对应的项目即为10个风险最大的项目，方案序号分别为10、37、47、50、51、57、60、64、66、74，而造成风险较大的原因大都是收购储备面积过大，总存储成本过高或预期收益较小。

最后，为了保证所建立模型的可行性以及计算结果的可靠性，我们对所建立的模型进行了检验。因为土地储备方案风险评估是一个决策问题，所以也可用层次分析法进行求解。于是我们又建立了层次分析法模型，利用MATLAB软件进行求解，得出影响土地储备风险的三个主要因素分别为收购储备面积，总收储成本和预期收益，这一结果验证了主成分分析模型的可行性和风险函数计算结果的可靠性。

参赛队号: 2900 Array

所选题目: C 题

英文摘要

Upon the problem that there are certain financial risks in land purchasing and banking, principal component analysis model and analytic hierarchy process model are established in this paper through comprehensive application of single variable analysis and multivariate statistical methods. EXCEL, MATLAB and C Language Program are used to solve and build the risk function of land banking projects. The data provided in Attachment 2 are statistically analyzed based on the risk function, so as to find out the ten projects with the biggest risks. Thereafter, the reasons leading to the risks of these ten projects are explained correspondingly.

First, the influence of single variable on the risks of land banking projects is analyzed. EXCEL is applied to draw the comparison diagrams of purchasing and banking area, dynamic recovery cycle, total purchasing and banking cost and prospective earnings for the 74 projects, so as to roughly find out the main factors related to the risks of land banking projects, that is, purchasing and banking area, total purchasing and banking cost and prospective earnings. After that, the cost and earnings of unit banking area are calculated with EXCEL, and the comparison diagrams of cost and earnings for unit banking area are drawn, so as to obtain the scope of difference in cost and earning of these 74 projects.

Second, the principal component analysis model is established, and MATLAB is used to calculate the correlation coefficient, thus more accurately deciding the main factors associated with the risks of land banking projects. The risk function of land banking projects is also decided, namely

S = 0.264 X1 + 0.422 X2 - 0.313 X3

Following that, the relevant data of 74 projects are substituted into the risk function of land banking projects: S = 0.264 X1 + 0.422 X2 -0.313 X3, so as to obtain 74 risk function values. These values are then input to C Language Program, which is designed to list the values in the descending order, to get the top ten values. So, the projects corresponding to these values are believed to be the top ten projects with the biggest risks. These projects are Project No. 10, No. 37, No. 47, No. 50, No. 51, No.57, No. 60, No.64, No. 66, and No. 74. The reasons for the big risks include too large purchasing and banking area, too high total banking cost or relatively low prospective earnings.

Finally, the model is tested for its feasibility and the reliability of the calculation results. Considering that risk evaluation of land banking projects is a decision-making problem, the analytic hierarchy process is resorted to. Therefore, the analytic hierarchy process model is built, and MATLAB is applied for solutions. The three main factors influencing the risks of land banking projects are land purchasing and banking area, total purchasing and banking cost and prospective earnings. This result proves the feasibility of the principal component analysis model and the reliability of the calculation results of the risk function.