基于ahp总结的风险损失模型

随着极端天气和自然灾害的发生，财产保险变得越来越昂贵。但保险公司的盈利能力并没有同步提高。这导致了业主负担能力和保险公司盈利能力的危机。因此，财产保险的可持续性受到了影响。我们的目的是适当地定位财产保险。使保险公司能够承受未来的索赔，并继续以健康的方式增长。

对于问题1，为了确定是否在极端天气和自然灾害频繁的地区投保，我们首先对收集到的数据进行预处理，如自然灾害造成的风险、脆弱性和财产损失。然后，基于层次分析法的思想，我们构建了一个CRITIC-KNN风险水平模型，并将其与成熟的灾害模型相结合，以获得每种灾害的年损失数据。两者共同构成了风险损失模型，CRITIC目标熵权法（以2020年为例）获得的权重分别为37.42%、12.92%、18.47%、16.82%和14.37%。选取美国俄亥俄州和中国四川进行模型验证，发现两者的WRI指数分别为3.86和5.88。然而，考虑到两者的财产损失情况，不建议投保。

对于问题3，通过改进模型，我们将社区财产的文化和经济价值添加到不符合保险条件的社区中。为社区提供保护机制，以保护其财产。首先，通过CRITIC-KNN算法，我们根据指标权重5.68计算了泸定大桥的总加权得分。然后，我们添加了文化和经济价值影响因素。我们重新使用CRITIC为影响因素分配权重值，并根据指标权重计算总加权分数4.48。随着分数的下降，风险水平降低，表明需要现场保护。否则，建议在另一个位置保护它。原始模型的计算结果在WRI类别中为5.68，风险等级为高风险。在WRI类别和中等风险水平下，改进模型的计算结果为4.48。这一地标对该地区具有巨大的文化和经济价值，应就地保护。

内容

1介绍   1

1.1背景   1

1.2对该问题的重述   2

1.3我们的工作   2

2模型准备  3

2.1.假设和正当理由  3

2.2符号  3

3、模型的建立及解决方案  4

3.1 Task1   4

3.1.1、数据分析和预处理： 4

3.1.2模型建立： 5

3.1.3模型求解  7

3.1.4对结果的分析与评价  10

3.2 Task2   11

3.2.1 模型建立：  12

3.2.2模型解决  14

3.2.3分析和结果评价  15

3.3 Task3   16

3.3.1 模型建立：  16

3.3.2模型解决  16

3.3.3分析和结果评价  18

3.4任务4：拯救泸定桥   18

3.4.2型号来源：  18

3.4.2模型解决  19

3.4.3分析和结果评价  19

4敏感性分析  20

5.对模型的评价  21

5.1优势   21

5.2弱点   21

6参考资料  21

7附录   1

Content

1 Introduction  1

1.1 Background 1

1.2 Restatement of the Problem 2

1.3 Our Work  2

2 Model Preparation 3

2.1 Assumptions and Justification 3

2.2 Notations 3

3 Model Establishment and Solutions  4

3.1 Task1  4

3.1.1 Data analysis and preprocessing：   4

3.1.2 Model Establishment:  5

3.1.3 Model Solving  7

3.1.4 Analysis and Evaluation of results  10

3.2 Task2 11

3.2.1 Model Establishment: 12

3.2.2 Model Solving  14

3.2.3 Analysis and Evaluation of results  15

3.3 Task3 16

3.3.1 Model Establishment: 16

3.3.2 Model Solving  16

3.3.3 Analysis and Evaluation of results  18

3.4 Task4：Saving the Luding Bridge 18

3.4.1 Model Source:  18

3.4.2 Model Solving  19

3.4.3 Analysis and Evaluation of results  19

4 Sensitivity analysis 20

5 Evaluation of the model  21

5.1 Strengths  21

5.2 Weaknesses 21

6 Reference 21

7 Appendix 1

1 介绍

1.1 背景

近年来，极端天气和自然灾害频繁发生。它给人类社会和自然环境带来了巨大的影响。极端天气 和自然灾害不仅造成了大量的人员伤亡和财产损失，而且对当地的经济和社会发展产生了深远的 影响。它导致了保险财产成本的上升，这导致了保险公司的盈利能力和业主的财务能力的危机。 因此，有必要加强对各地区极端天气和自然灾害的研究和预测，以更好地应对风险和保护财产。

Figure 1:Global Disaster Map

从保险公司的角度来看，由于极端天气和自然灾害造成的财产损失，保险公司需要支付巨额索赔 。为了补偿索赔成本的增加，保险公司可能会提高保费，这会影响保险市场的稳定。由于索赔成 本和保费的增加，保险公司可能会影响其承保能力，减少了其在市场上的承保范围和数量。保险 公司应加强风险管理，提高其对灾难的适应能力，并与政府和其他组织更密切地合作。

从业主的角度来看，随着极端天气和自然灾害的频繁发生，业主可能会更加意识到风险管理和保 险的重要性。他们可以选择更全面的保险计划或采取其他风险管理措施。极端天气和自然灾害可 能使业主遭受财产损失或完全损失，从而增加业主的风险。业主还需要更加重视风险管理，并采 取适当措施保护其财产。

从被保险财产的角度来看，由于极端天气和自然灾害的频繁发生，对被保险财产的损害更加严重 。为了加强对被保险对象的保护，必须实现长期的保护。提倡开展气候相关政府培训，提高世界 人民意识，促进生态周期建设，实现可持续发展。

1.2 Restatement of the Problem

Considering background information and restricted conditions identified in the problem statement, we need to solve the following problems.

Problem: 1:Extreme weather events and natural disasters increase the risk of property damage.Insurance companies need higher premiums to cover risks, and the risk of claims payouts increases.For sustainable development of the property insurance industry, develop a model for insurance companies to determine when they can and cannot underwrite.Demonstrate the model through two regions in different continents that have experienced extreme weather or natural disasters.

Problem: 2:The insurance environment is undergoing with the gradual increase in extreme weather events and natural disasters.Adjust your model to provide appropriate advice for future real estate decisions.Determine whether sites are suitable for development and how to build properties more resistant to disasters.

Problem 3:Develop a protection model to determine the level of protection for properties not recommended for insurance due to cultural and economic factors.

Problem 4:Choose a coordinate location and use the model you have developed to evaluate that location.Based on the evaluation results, write a proposal to the community about the future development plans, timeline, and development costs for the site.

Figure 2:The Overall Process Of The Problem

1.3 Our Work

首先，针对问题 1，为了确定在极端天气和自然灾害频繁发生的地区是否应该进行承保，我们建立了保险模型，对收集到的数据进行预处理，例如自然灾害造成的风险、脆弱性、财产损失等。通过 CRITIC-KNN 算法，为影响因素分配权重值。我们使用指标权重计算两个区域的总加权分数。最后，确定是否应为该站点投保。

其次，改进问题 1 中设计的模型。在选定的区域建造房地产并使其具有抗灾能力将改变脆弱性影响因素。然后，我们使用 ARIMA 时间序列模型来预测影响因子的未来值。最后，通过 CRITIC-KNN 算法，我们获取所选区域的未来加权分数。根据评估结果，向社区撰写关于该站点未来开发计划、时间表和开发成本的建议。

接下来，对于问题 3，继续改进模型。通过将社区内财产的文化和经济价值因素纳入，为不符合保险资格的社区提供保护机制。使用 CRITIC-KNN 算法，计算改变影响变量后的总加权得分，以确定如何保护社区中的财产。

2模型准备

2.1假设和正当理由

·假设1：将极端天气和自然灾害的发生时间限制在2011年至2020年期间。

论证1：限制时间的目的是为了简化问题，使模型更易于管理，并提高计算效率。极端天气和自然 灾害的时间范围太宽，导致了一些计算。过去距离太遥远的数据可能会对预测结果产生不利影响

。

·假设2：假设极端条件和自然灾害类型包括暴雨、干旱、地震、洪水、山体滑坡、火山爆发和 野火。

理由2：极端条件和自然灾害有多种形式。根据我们的数据处理，全球模型中包含的8个自然灾害 和极端天气事件都是发生频率较高的事件。使我们的模型更普遍地适用。

·假设3：经济正处于一种自然发展的状态

理由3：首先，我们认为国际贸易不受国际形势的影响，而国际形势对经济有重大影响。其次，我 们假设没有类似的经济危机情况，且经济的异常波动不利于该数据的应用，这将会导致较大的误 差。

2.2符号

3 模型的建立及解决方案

3.1 Task1

关于问题1，我们在联合国官方网站和各大洲和国家的政府门户网站上获得了2011年至2020年期间 五大洲约180个国家自然和气候灾害的频率、损失和伤亡的数据。通过这些数据，分析国家的综合 风险指数，对其风险进行分类，结合当地的财产损失，综合判断当地的风险和损失，构建风险损 失模型，帮助保险公司做出更好的商业决策。

1.13 数据分析和预处理：

首先，在本期中，我们主要被称为、处理和分析了三个数据集。

第一个数据集是关于全球灾害风险的年度技术报告，世界风险报告主要关注与灾害风险管理相关 的各种主题，以及用于评估世界上许多国家的极端自然事件灾害风险的指数。世界风险指数由某 一地区的极端自然灾害和暴露水平以及该区域的社会脆弱性组成。社会脆弱性分为某一地区对极 端自然事件的易感性、缺乏应对能力和缺乏适应性。

该指标从灾害发生的可能性、灾害发生前、灾害发生中、灾害发生后的因素、多个方面评价某一 地区的极端自然事件灾害指数，对区域灾害的评价具有重要意义。一个国家在世界风险指数上的 指数得分越高，其国家的灾害风险就越高。该数据集全面地展示了世界各国的灾害风险，因此我 们使用来自世界风险报告的数据集作为我们研究的基础。

图 3：全局灾难分类 图 4 :灾难趋势图

在此数据集的基础上，我们使用其他两个数据集的灾害损失和频率的详细数据来整合和优化数据，并使用这些数据来分析每个大洲和国家的各种灾害的比例，以及每个国家每次灾害的经济损失。这是我们主要使用的三个数据集，我将详细介绍我们的数据预处理步骤和一些重要的数据可视化成果。

由于数据集中缺乏某些信息，我们使用Python在预处理过程中搜索和修改数据集中的离群值，并 删除缺失的值。使该数据集更加准确和全面，提高数据的准确性和价值，并促进减少后续机器学 习中的错误。在第一个数据集中，我们需要主要关注诸如“世界资源研究所”、“暴露 ”、“脆 弱性 ”、“敏感性 ”、“响应能力不足 ”和“适应能力不足 ”等条目。这些条目科学地分析了在 客观和主观条件下的局部风险指数和风险水平，并充分考虑了时间和空间的重要性。

通过数据可视化，我们可以得到以下图像：

图5：暴露水平与风险评分之间的相关性分析

This graph tells us that there is a strong correlation between exposure level and risk score. Of course, the correlation coefficients we obtained later also confirm this point. In addition to the strong correlation between exposure level and risk, we obtained a strong correlation between the exposure index and the number of disasters that occurred in the area by integrating the data table. This reflects the correctness of our data integration, and we can predict the number of disasters that occurred in the year through the change pattern of the index.

Of course, with the frequency of disasters occurring, each continent and country will have a tendency to predict what kind of disasters will occur, how many times such disasters will occur, and the risks will be reduced accordingly. It is not only an economic issue, but also a safety issue.The following graph are the

disaster "tendency" graphs obtained after data integration:

3.1.2 Model Establishment:

For such problems, we can convert evaluation problems into classification problems, which can better directly determine their risk level. For higher and very high-risk areas, we can ignore their insurance coverage, but for medium, low, and very low-risk areas, we need to combine local disaster losses to make a final judgment on whether to insure locally. This can effectively avoid complex numerical calculations.

According to the characteristics of the data, it has temporal characteristics and can be divided into training and testing sets by year. After integrating and optimizing the dataset, it can be used for regression analysis

using the KNN algorithm in machine learning. It determines the nearest neighbor samples based on their eigenvalues, calculates distances, and makes classification decisions based on their labels. The core idea of the KNN algorithm is to assume that neighboring samples that are most similar to the target sample have similar labels.As a representative algorithm of supervised learning, the approximate steps are as follows:

·Exploratory analysis of EDA data ·Feature engineering

·Splitting the dataset into training and testing sets

· Training model: Use the training set to train the model

·Test set: Use the obtained training model to test the test set6. Model evaluation: accuracy

For KNN algorithm, there are three unique elements compared to other machine learning algorithms that can provide more accurate instances in the training set.

·Distance: This question uses Euclidean distance

·K value: Using loss function to reduce K value

·Classification Decision: Weighted Optimization CRITIC

(1)

(2)

Table 1 ：Objective entropy weight analysis

When dividing levels, we used Analytic Hierarchy Process (AHP), which is a quantitative method used to handle complex decision-making problems. It decomposes the problem into different levels of criteria and sub criteria, and then compares them pairwise to determine their importance weights. In this issue, the risk index can be divided into two criteria: objective and subjective. That is, the exposure index and vulnerability belong to the first level, and the second level is the three components of the vulnerability index: sensing ability, coping ability, and adaptability.

The AHP-KNN algorithm uses the weight vector of AHP as the weight attribute of the KNN algorithm to improve classification decision-making. Specifically, it first uses AHP to determine the importance weight of each feature and applies these weights to the feature vectors in the KNN algorithm. Then, by calculating the distance between the target sample and each sample in the training set, classification decisions are made based on the nearest neighbor label.

Use Analytic Hierarchy Process to determine the weight of each factor. The Analytic Hierarchy Process allows us to establish a judgment matrix by comparing the importance of each factor pairwise. With the help of expert opinions or relevant statistical data, we can rate each factor to reflect its relative importance to other factors. Through the feature vector method, we can calculate the weight of each factor and represent it as w1, w2, w3, w4, and w5。

Use the K-nearest neighbor algorithm to calculate the disaster risk index.

Assuming we have a training dataset that includes data on exposure, vulnerability, susceptibility, lack of response and adaptation in different regions, as well as corresponding disaster risk level labels.Specifically, we will use the following formula to calculate the disaster risk index for a certain region:

RiskIndex = KNN(w1 * x1, w2 * x2, w3 * x3, w4 * x4, w5 * x5 ) (3)

x1, x2, x3, x4, and x5 represent the values of exposure, vulnerability, susceptibility, lack of coping ability, and lack of adaptability in the region.

w1, w2, w3, w4, and w5 are the weights of the corresponding factors, respectively.By combining the AHP method to determine weights and the K-nearest neighbor algorithm for disaster risk index calculation, various factors can be comprehensively considered to obtain a relatively accurate disaster risk assessment result.

In the process of reducing the k-value, we found that the Analytic Hierarchy Process (AHP) did not achieve ideal prediction results because there were always human factors in the process of dividing levels, and some correlations may be ignored, leading to a decrease in accuracy and poor model performance.

So we chose an objective entropy weighting method, CRITIC, which is a method used to evaluate models. This method conducts correlation analysis on multiple indicators of model performance to determine the importance of each indicator to model performance.

The CRITIC method includes the following steps: ·Determine evaluation

·indicatorsEvaluation model

·Calculate correlation coefficient:

·Determine the importance of indicators ·Analysis results

3.1.3 Model Solving

In the KNN algorithm, the exposure index, vulnerability index, sensitivity index, lack of coping ability index, and lack of adaptability index are used as independent variables, while the wri category is used as the dependent variable. The training set ratio is set to 0.8, the number of K neighboring samples is set to 5, and the sample voting weight is set to proportional voting weight. The neighbor search method is automated, and the distance calculation is performed using the Euclidean distance calculation method for KNN modeling.The final model achieved an accuracy of 45.95% on the test set, an accuracy (comprehensive) of 62.93%, a recall (comprehensive) of 45.95%, and an F1 score (comprehensive) of 0.49. The model effect is relatively poor.

Using the CRITIC model, assuming that the dataset consists of n data samples, m indicators are defined based on this dataset and abstracted into mathematical language as follows: X1, X2... Xn ...

1 ·Data normalization processing

The types of indicators are usually divided into four types: positive indicators, negative indicators, intermediate indicators, and interval indicators.

The calculation method for normalizing positive indicators is:

The calculation method for normalizing negative indicators is:

The calculation method for normalizing intermediate indicators is:

The calculation method for normalizing interval indicators is:

(4)

(5)

(6)

(7)

(8)

CRITIC evaluates and decides how to allocate weights based on the differences in values within each indicator. It is believed that the larger the standard deviation, the more information the indicator can reflect, and therefore, more weight should be assigned to this indicator.

The CRITIC method believes that the larger the value of the linear positive correlation coefficient between indicators, the smaller the conflict, and therefore, smaller weights should be assigned.

·The carrying capacity of information and specific calculation methods Calculate indicator weights：

Table 2:Factor indicator weighting table

Figure 6 ：Empowerment Comparison Chart

According to the CRITIC model, assign weights to variables and recalculate the k value based on the test results to verify the effectiveness of CRITIC.The accuracy is 80.73%

Figure 7 ：Model evaluation renderings

The above is the "risk" section of the risk loss model we want to establish, and the process of establishing the other "loss" section is as follows:

Through data integration, we found that the disaster losses in a region are related to multiple aspects, such as the number of deaths, damage level, duration, and very important types of disasters. Due to the large number of missing values in the disaster insurance amount data from 2011 to 2020, which cannot be supplemented by algorithms, we can only determine an economic risk in this region based on its losses.

Disaster modeling, also known as cat modeling, is the process of using computer-aided calculations to estimate the potential losses caused by catastrophic events such as hurricanes and earthquakes.

Table 3 ：Model results analysis table（2011-2020）

The output of the cat model is an estimate of the model's prediction of losses related to a specific event or set of events. When running a random model, the output is a random loss distribution or a set of events that can be used to create a loss distribution. The loss distribution can be calculated as the possible maximum loss and the average annual loss.

3.1.4 Analysis and Evaluation of results

In response to this issue, we have selected Asia and the Americas as the two continents, China and the United States in Asia, which have rich landforms and large land areas. In addition, the two countries are in different development situations. China is a developing country and the United States is a developed country, and there are certain differences in the level of disaster response between the two countries. Overall, the vulnerability index is more informative and representative.

By analyzing the frequency and types of disasters that occur in each continent and country, we can infer whether there is a disaster situation and level in that area at a certain time. To determine whether to insure in that area, we first use the first CRITIC-KNN risk assessment model based on the Analytic Hierarchy Process to obtain the WRI index and types for China and the United States:

Table 4 ：KNN Risk Assessment WRI Index and Classification

Specific classifications can be obtained through weighted distance:

Table 5 ：Weighted distance analysis evaluation scale scale

Figure 8 ：Diagram of risk versus population density

The United States and China can obtain risk indices WRI of 3.76 and 5.87 through risk models, with a risk level of intermediate. Therefore, it is necessary to combine the second disaster model to determine their property losses. Based on the tendency of disasters and the losses caused by this tendency, it can be seen from the image that the loss index of Ohio in the United States is relatively high. Therefore, when planning insurance plans for Ohio in the United States, insurance companies should carefully consider and not insure.

For China, it is also necessary to consider the property loss index and property loss level. After data research, it can be found that China's property damage has been fluctuating around the world's property losses. Due to the frequent occurrence of disasters every year, taking Sichuan Province as an example, local disasters occur more frequently, but property losses are at a moderate level, and insurance needs to be carefully considered.

3.2 Task2

In the second question, we need to clarify a premise that our discussion object is already in line with the requirements of insurance companies for insurance, which means that their risk index classification

evaluation and loss index classification evaluation are at a relatively low level, because adding a community will inevitably bring some population and ecological pressure to the local area. For example, an increase in population will lead to an increase in the "lack of sensitivity index". In other words, an increase in population will increase the local "entropy value", which is the degree of chaos.

In the initial stage of establishing the model, we need to know the local population density and economic situation, add new influencing factors to the first question model, objectively assign weights, adjust the k value, improve accuracy, and obtain a new risk loss model.

Compared to the first question, we need to pay more attention to one issue, "time", which means we need to predict and use the predicted data to determine how we should adjust our insurance plan. There are mainly three types of adjustments, of course, the adjustment of premiums and the strengthening of intervention are not conflicting, but the focus is different.

·Waiver ofInsurance

In this question, we will take Beijing, China as an example. Objectively speaking, Beijing belongs to a lower risk area. Subjectively speaking, Beijing's vulnerability does not match its economic development status. For the capital, there is great room for improvement in perception, response, and adaptability. Beijing's vulnerability is closely related to local population density, economic development, and other factors.

Figure 9 ：Population density map of Beijing, China

3.2.1 Model Establishment:

The ARIMA model can use the historical information of the data itself to predict the future. This includes regression models (AR) and moving average models (MA). The AR model has the advantage of having data with long historical trends and can capture trends for prediction. However, due to its dependence on history, it may ignore the complexity of the real situation. Therefore, by combining the MA model, it can handle temporary sudden changes.

The ARIMA model assumes that label values fluctuate around a major trend over time, where the trend is influenced by historical labels and the fluctuation is influenced by accidental events over a period of time, and the major trend itself may not necessarily be stable.

Basic steps:

·Perform stationarity processing on non-stationary time series data to obtain a stationary sequence ·Model research:

·Select Model ·Definite order

Partial autocorrelation coefficient (determining order): Considering the presence of random errors, the partial autocorrelation coefficient may not be strictly 0 after p-order delay, but fluctuates within a small range around 0.

·Fixed order optimization

The FPE criterion assumes that AR (p) is the fitting model, and 0，1 ......p are the

autocorrelation functions of each order sample in the sequence. The final prediction error can be expressed as：

(10)

·Parameter estimation

A certain criterion estimates the parameter .

2

a 1 , a2 ......ap , σ

p+1. If the order p in the model is

also used as an estimated parameter, the number of parameters to be estimated will be p+2.

εt = Xt - a1Xt -1 - a2 Xt -2 - ...... - apXt -p	(11)
	(12)
Least squares estimation (minimum sum f squared residuals)： o
j = xj - ( 1xj -1 + 2 xj -2 + ...... + pxj -p )	(12)

Usually referred

Obtain the following linear equation system:

Y = Xa + ε

The objective function of the sum of squared residuals can be expressed as: S (a) = (Y - Xa )T (Y - Xa ) = YTY - 2YTXa + aTXT Xa

Taking the derivative of parameter a from the above equation and setting it to 0 yields:

(14)

(15)

(16)

Therefore, the least squares estimate of parameter a is:

At this point, the least squares estimate of the error variance is:

·Model validation

Including validity and significance testing of the model:

(17)

(18)

·Model prediction

The main purpose of time series analysis is to predict the next time series value Xt+1 or the sequence value Xt+k after k steps, given a time series X1, X2... Xt。

3.2.2 Model Solving

When solving this problem, we will continue to use the machine learning algorithm from the first problem, but due to the addition of future developments, we need to establish a machine learning based time series prediction model.

In this section, in addition to focusing on time, we also need to adjust the insurance model for the situations that arise. In this section, we need to predict the level of risk losses in the area and judge whether to insure or increase or decrease premiums based on the new level of risk losses.

This chart shows the changes in insurance premiums in the Beijing region from 2006 to 2016 (approximately 800 cases per year):

Figure 10：2006~2016 Beijing premium change chart

In the first question, we observed a stable trend of WRI values over time using violin plots and scatter plots, without significant fluctuations. In this question, we analyzed and predicted WRI index, exposure index, and vulnerability using a time series model.

The following data is presented using the WRI index as an example:

Based on the variable WRI, when the difference is of order 0, the significance P-value is 0.000 * *, showing significance at the horizontal level. Rejecting the null hypothesis, this series is a stationary time series. When the difference is of 1st and 2nd order, the significance P-value is 0.000 * * *, showing significance at the horizontal level. Rejecting the null hypothesis, this sequence is a stationary time series.

Verify the model:

Based on the variable WRI, the model formula is as follows:

y(t) = 0.716 + 0.906* y(t -1) - 0.265*ε(t -1) （19）

The goodness of fit R of the model ² At 0.678, the model performs well. The predicted results for the next 7 years (2021-2027) in Beijing are 1.331711410151208, 1.9230514728671209, 2.4588635560156,2.9443618461786567,3.384270904589377,3.782871649040758,and4.1440430103471 1, respectively.

Of course, this completely disregards factors such as population and economic pressure. However, according to the reality, the addition of communities will inevitably have consequences for local vulnerability. Therefore, we have introduced a new influencing factor, "lack of urban capacity," as a factor that constitutes urban vulnerability. This is also why we continue to use the idea of the first level analysis method, and based on the population density of Beijing, The level of economic development is once again using the CRITIC objective weighting method to re assign weights to influencing factors.

The empowerment results are shown in the following figure:

Figure 11：Weights of six factors

Using the new weights to recalculate the WRI index and substituting it into the time series model again, the result is as follows: the goodness of fit R of the model ² A score of 0.869 indicates excellent performance. The predicted WRI index for Beijing in the next 7 years is 5.33, 6.92, 4.45, 5.94, 5.38, 6.78, and 8.14, respectively.

3.2.3 Analysis and Evaluation of results

We have learned from the above data that currently, the density of communities within the third ring road of Beijing is relatively high, and the construction of communities will have a certain degree of damage to the stability of the community. Based on the predicted data, 2023 is more suitable for community investment and construction, but the next few years are not suitable for real estate development and construction, with higher risks and lower cost-effectiveness.

According to data, in recent years, premiums in Beijing have shown an upward trend, and the number of high premiums is increasing. Therefore, appropriately increasing scrapping can hedge against the high risks in Beijing.

3.3 Task3

3.3.1 Model Establishment:

The Luding Bridge in Luding County, Sichuan Province, was selected as a research landmark.Due to the frequent earthquakes in the area where the Luding Bridge stands, the insurance model does not recommend that the Luding Bridge be insured.But the Luding Bridge is an essential embodiment of China's revolutionary spirit. The cultural and economic value of Luding Bridge makes leaders hesitate.

Figure 12：Schematic diagram of the earthquake in Sichuan Province, China

Invoke the knn algorithm, Critic model, and disaster model in Problem 1.CRITIC uses the differences in the values within each indicator to evaluate and decide how to allocate weights.It is considered that the greater the standard deviation and the more information the indicator can reflect, the higher weight should be given to the indicator.The knn algorithm gives a score and risk level for the combined effect of risk and loss.

Then, the original model is improved by adding the two indicators of culture and economy.CRITIC recalculates the weights of each index.Using the knn algorithm obtaine the score and risk level.Comparing the results of the original and improved models, a lower WRI category score and risk level indicates that the landmark is valuable to the site and should be preserved in place, and vice versa.

3.3.2 Model Solving

The weights of each index of Luding Bridge in Luding County, Sichuan Province were obtained with CRITIC.

Table 6:Weight distribution table of each index of Luding Bridge, Luding County, Sichuan Province