Problem Chosen 选择的问题
E
MCM/ICM 管理和监测/信息和通信管理
Summary Sheet 汇总表
Team Control Number 团队控制编号
Veils of Uncertainty: Weaving Risk into the Tapestry of Preservation Under the Weather's Watch Summary 《不确定的面纱：在天气监视下将风险编织到保护工作的织锦中》摘要
As the tapestry of nature weaves its unpredictable patterns, humanity’s quest for stability becomes ever more pressing. In the shadow of uncertainty, we find resilience, crafting shields against the tempests of fate. 当大自然的织锦编织出变幻莫测的图案时，人类对稳定的追求也变得愈发迫切。在不确定性的阴影下，我们找到了韧性，打造了抵御命运风暴的盾牌。
First, we establish a Risk Analysis model to comprehensively assess the Expected Annual Loss (EAL) from extreme weather in terms of population, building, and agriculture. The assessment for each aspect is calculated from three perspectives: natural hazard exposure, Historic Loss Ratio, and the likelihood risk factor of natural hazard annualized frequency. Community Risk Factor (CRF) is calculated from social vulnerability and community resilience. EAL and CRF are used to quantify the risk levels of various regions and rank them using the K-means algorithm, resulting in a risk level map of the United States. 首先，我们建立了一个风险分析模型，从人口、建筑和农业三个方面全面评估极端天气造成的预期年损失（EAL）。各方面的评估从三个角度进行计算：自然灾害风险暴露、历史损失率和自然灾害年化频率的可能性风险系数。社区风险系数 (CRF) 是根据社会脆弱性和社区恢复力计算得出的。EAL 和 CRF 用于量化不同地区的风险水平，并使用 K-means 算法对其进行排序，从而绘制出美国的风险水平图。
Second, we develop a Risk-incorporated Capital Asset Pricing Model (CAPM) to aid insurance companies in underwriting decisions. This model combines market return rates, the risk-free rate, and bankruptcy theory with a 10%10 \% bankruptcy probability to set insurance rates. It evaluates if the region’s residents can afford these premiums, providing decision-making advice for insurance companies. 其次，我们建立了风险纳入资本资产定价模型（CAPM），以帮助保险公司做出承保决策。该模型将市场收益率、无风险利率和破产理论与 10%10 \% 破产概率相结合，以确定保险费率。它可以评估该地区的居民是否能够负担得起这些保费，从而为保险公司提供决策建议。
More specifically, we apply our Risk-incorporated Capital Asset Pricing Model in Los Angeles and Gorontalo. In Los Angeles, insurance companies see high profits and low risks. However, in Gorontalo, the required premium for $10,000\$ 10,000 coverage is $342.745\$ \mathbf{3 4 2 . 7 4 5}, beyond local affordability. We recommend insurance securitization and partnerships with local governments to reduce premiums. Consequently, Gorontalo residents could pay just $137.25\mathbf{\$ 1 3 7 . 2 5} annually, with companies projecting $245\mathbf{\$ 2 4 5} million in revenue. 更具体地说，我们将风险纳入资本资产定价模型应用于洛杉矶和戈伦塔洛。在洛杉矶，保险公司看到的是高利润和低风险。然而，在戈伦塔洛， $10,000\$ 10,000 保险所需的保费为 $342.745\$ \mathbf{3 4 2 . 7 4 5} ，超出了当地的承受能力。我们建议保险证券化，并与地方政府合作降低保费。因此，戈伦塔洛居民每年只需支付 $137.25\mathbf{\$ 1 3 7 . 2 5} ，公司预计可获得 $245\mathbf{\$ 2 4 5} 万的收入。
Third, we establish a Building Preservation Model, selecting seven secondary indicators such as the annual number of visitors and construction cost, and three primary indicators: cultural values and community influence, economy, and history. These are weighted using the Sperman-CRITIC algorithm and AHP method to calculate building value, combined with risk levels to determine the preservation level of buildings. Based on the preservation level, the community’s investment and measures for building protection can be determined. 第三，建立建筑保护模型，选取年游客量、建筑成本等七个二级指标和文化价值与社区影响、经济、历史三个一级指标。利用 Sperman-CRITIC 算法和 AHP 方法对这些指标进行加权，计算出建筑物的价值，再结合风险等级，确定建筑物的保护等级。根据保护级别，可以确定社区对建筑保护的投资和措施。
Then our models inform investment and protection strategies for Tokyo Tower, acknowledging its value and the necessity of preservation in an earthquake zone. We communicate these findings and propose protection measures to the Tokyo Tower community. 然后，我们的模型为东京塔的投资和保护战略提供信息，承认其在地震带的价值和保护的必要性。我们将向东京塔社区传达这些发现并提出保护措施。
Finally, we analyze the sensitivity and robustness of our models, the models can change the insurance rate sensitively according to the change of the market predicted return and the slight error of the risk factor calculation will not affect the models’ result, which verifies the sensitivity and robustness of our models. In addition we analyze the strengths and weaknesses of the models. 最后，我们分析了模型的灵敏性和稳健性，模型可以根据市场预测收益率的变化灵敏地改变保险费率，风险系数计算的微小误差也不会影响模型的结果，这验证了模型的灵敏性和稳健性。此外，我们还分析了模型的优缺点。
1 Introduction … 4 1 导言 ... 4
1.1 Problem Background … 4 1.1 问题背景 ... 4
1.2 Restatement of the Problem … 4
1.3 Our Work … 4 1.3 我们的工作 ... 4
2 Assumptions and Justifications … 5
3 Notations … 5 3 注释 ... 5
4 Insurance Pricing and Decision Model … 6 4 保险定价和决策模型 ... 6
4.1 Data Collection … 6 4.1 数据收集 ... 6
4.2 Risk Analysis … 6 4.2 风险分析 ... 6
4.2.1 The Expected Annual Loss(EAL) … 6
4.2.2 Community Risk Factor … 7 4.2.2 社区风险因素...... 7
4.2.3 Risk Calculation … 8 4.2.3 风险计算...... 8
4.3 Insurance Premium … 9 4.3 保险费 ... 9
4.4 Measures … 13 4.4 措施 ... 13
4.4.1 Insurance Securitization … 13 4.4.1 保险证券化 ... 13
4.4.2 Co-operation with the Government … 13
4.4.3 The Implementation of Measures … 14
4.5 Real Estate Decision Making … 14 4.5 房地产决策 ... 14
5 Building Preservation Model … 16
5.1 Building Value Quantification … 16
5.1.1 Indicators Determination … 16
5.1.2 Weight Calculation … 17 5.1.2 重量计算 ... 17
5.1.3 Quantitative Results of Building Values … 19
5.2 Determination of protection measures … 20
5.2.1 Measure Score … 20
5.2.2 Score of Protection Measures … 20
5.2.3 Mentoring for Community Leaders … 20
6 Landmark Case Analysis … 21 6 里程碑案例分析 ... 21
6.1 Insurance Pricing for Tokyo Tower … 21 6.1 东京塔的保险定价...... 21
6.2 Architectural Value of Tokyo Tower … 21 6.2 东京塔的建筑价值...... 21
7 Sensitivity and Robustness Analysis … 22
7.1 Sensitivity … 22
7.2 Robustness … 23
8 Model Evaluation … 23 8 模型评估 ... 23
8.1 Strengths … 23 8.1 优势 ... 23
8.2 Weaknesses … 23
References … 23 参考文献 ... 23
1 Introduction 1 引言
1.1 Problem Background 1.1 问题背景
Extreme weather events are becoming more frequent due to climate change. As the economic costs of disasters rise, how should the insurance industry respond to losses? Extreme weather events cause untold human suffering but and ever-growing economic costs. 由于气候变化，极端天气事件越来越频繁。随着灾害造成的经济损失不断增加，保险业应如何应对损失？极端天气事件给人类带来了无尽的苦难，但也造成了不断增长的经济损失。
Catastrophic risks consequently cause a variety of problems for insurers. First, because the losses arise from a small number of lumpy events, the insurer may not have sufficient resources to cover the losses. Less dramatically, the firm may suffer losses well in excess of the value of the premiums that it charged for the coverage. In the absence of adequate reinsurance, the firm may go bankrupt or may choose to exit a state in which there is a substantial exposure to such catastrophic risks. The unexpected catastrophes or blockbuster events maybe raise the rate that firms charge for insurance. Thus, for any given number of policies written, the total premiums will rise ^([1]){ }^{[1]}. 因此，巨灾风险给保险公司带来了各种问题。首先，由于损失是由少量的偶发事件造成的，保险公司可能没有足够的资源来弥补损失。更严重的是，公司蒙受的损失可能远远超过其收取的保险费的价值。在没有足够的再保险的情况下，公司可能会破产，或者可能会选择退出存在大量此类灾难性风险的国家。意想不到的灾难或大事件可能会提高公司的保险费率。因此，对于任何给定数量的保单，总保费都会上升 ^([1]){ }^{[1]} 。
The impact of natural disasters is equivalent to a $520\$ 520 billion loss in annual consumption, and forces some 26 million people into poverty each year. Given the gradual increase in the number of extreme-weather events in the world, how to realize the sustainability of property insurance is a great challenge we need to address. 自然灾害造成的影响相当于每年十亿 $520\$ 520 人的消费损失，每年迫使约 2600 万人陷入贫困。在全球极端天气事件逐渐增多的情况下，如何实现财产保险的可持续发展，是我们需要应对的巨大挑战。
1.2 Restatement of the Problem 1.2 问题的重述
Considering the background information and restricted conditions identified in the problem statement, we need to solve the following problems: 考虑到问题陈述中确定的背景信息和限制条件，我们需要解决以下问题： >> Problem 1: The property insurance industry faces a crisis from increased extreme weather events caused by climate change, leading to higher claims and premiums. >> 问题 1：由于气候变化导致极端天气事件增多，财产保险业面临危机，从而导致索赔和保费增加。 >> Problem 2: Insurance companies must decide on underwriting policies in weather-affected regions, balancing risk and long-term viability. >> 问题 2：保险公司必须决定在受天气影响的地区承保，平衡风险和长期生存能力。
Problem 3: Participants are tasked with creating a model to assist in underwriting decisions and a preservation model for community leaders to protect significant buildings. 问题 3：参与者的任务是创建一个模型，以协助作出承保决定，并为社区领导人创建一个保护模型，以保护重要的建筑物。 >> Problem4: The models should be applied to specific areas and a historic landmark, with recommendations for future insurance and preservation strategies. >> 问题 4：模型应适用于特定区域和历史地标，并就未来的保险和保护战略提出建议。
1.3 Our Work 1.3 我们的工作
In order to clearly illustrate our work, we draw the flowchart Figure 1. 为了清楚地说明我们的工作，我们绘制了图 1 流程图。
Figure 1: Our work 图 1：我们的工作
2 Assumptions and Justifications 2 假设和理由
Considering those practical problems always contain many complex factors, first of all, we need to make reasonable assumptions to simplify the model, and each hypothesis is closely followed by its corresponding explanation: 考虑到实际问题总是包含许多复杂的因素，我们首先需要做出合理的假设来简化模型，而每一个假设都紧跟着相应的解释：
Assumption: The data we use are accurate and valid. 假设：我们使用的数据准确有效。
Justification: Our data is collected from the World Bank and some other official web sites and research papers. it’s reasonable to assume the high quality of their data. 理由我们的数据来自世界银行和其他一些官方网站及研究论文。
Assumption: The regions under study will remain peaceful and stable, with no significant events other than natural disasters occurring in the foreseeable future. 假设：所研究的地区将保持和平与稳定，在可预见的将来不会发生除自然灾害以外的重大事件。
Justification: A stable capital market environment provides a predictable framework within which we can project our expected returns. It is important to note that this assumption does not negate the potential impact of natural disasters. 理由：稳定的资本市场环境为我们预测预期回报提供了一个可预测的框架。值得注意的是，这一假设并不否定自然灾害的潜在影响。
Assumption: The estimated figures for each region represent an average level of performance or condition for that area. 假设：每个地区的估计数字代表了该地区的平均绩效水平或状况。
Justification: For the purposes of this study, treating each region as a cohesive entity allows for a more streamlined analysis. This methodological approach simplifies the complexity inherent in regional studies by focusing on aggregate data, thereby providing a generalized view of each area’s performance or condition. 理由：就本研究而言，将每个地区视为一个整体，可以使分析更加简洁。这种方法侧重于综合数据，简化了区域研究中固有的复杂性，从而提供了对各地区绩效或状况的总体看法。
3 Notations 3 备注
The key mathematical notations used in this paper are listed in Table 1. 表 1 列出了本文使用的主要数学符号。
Table 1: Notations 表 1：符号
Symbol 符号
Description 说明
EAL
Expected Annual Loss 预期年度损失
SV
Social Vulnerability 社会脆弱性
CR
Community Resilience 社区复原力
CRF
Community Risk Factor 社区风险因素
HLR
Historic Loss Ratio 历史损失率
Symbol Description
EAL Expected Annual Loss
SV Social Vulnerability
CR Community Resilience
CRF Community Risk Factor
HLR Historic Loss Ratio| Symbol | Description |
| :--- | :--- |
| EAL | Expected Annual Loss |
| SV | Social Vulnerability |
| CR | Community Resilience |
| CRF | Community Risk Factor |
| HLR | Historic Loss Ratio |
There are some variables that are not listed here and will be discussed in detail in each section. 还有一些变量没有在此列出，将在各章节中详细讨论。
4 Insurance Pricing and Decision Model 4 保险定价和决策模型
Database Names Database Websites
Los Angeles https://geohub.lacity.org/
The National Risk Index National Risk Index | FEMA.gov
Bureau of the Census https://data.census.gov/
South Carolina https:////www.sc.edu//
World Bank https://// data.worldbank.org/| Database Names | Database Websites |
| :--- | :--- |
| Los Angeles | https://geohub.lacity.org/ |
| The National Risk Index | National Risk Index \| FEMA.gov |
| Bureau of the Census | https://data.census.gov/ |
| South Carolina | $\mathrm{https}: / / \mathrm{www} . \mathrm{sc} . \mathrm{edu} /$ |
| World Bank | $\mathrm{https}: / /$ data.worldbank.org/ |
4.2 Risk Analysis 4.2 风险分析
4.2.1 Expected Annual Loss (EAL) 4.2.1 预计年度损失（EAL）
The EAL value are in units of dollars, representing the community’s average economic loss from natural hazards each year. EAL is calculated using a multiplicative equation that considers the consequence risk factors of natural hazard exposure, HLR (Historic Loss Ratio), and the likelihood risk factor of natural hazard annualized frequency. The EAL value for each consequence type is calculated by multiplying the exposure value of an area by the estimated annualized frequency and the HLR. EAL 值以美元为单位，代表社区每年因自然灾害造成的平均经济损失。EAL 采用乘法等式计算，该等式考虑了自然灾害暴露的后果风险因子、HLR（历史损失率）和自然灾害年化频率的可能性风险因子。每个后果类型的 EAL 值都是通过将一个地区的暴露值乘以估计年化频率和 HLR 计算得出的。
EAL=" Exposure "xx" Annualized Frequency "xx HLRE A L=\text { Exposure } \times \text { Annualized Frequency } \times H L R
The total EAL value for each hazard type is the sum of three different types of consequences: population §, building (B), and agriculture (A). 每种危害类型的总 EAL 值是三种不同类型后果的总和：人口 §、建筑 (B) 和农业 (A)。
EAL_("Hazard Type ")=EAL_("Hazard Type "(P))+EAL_("Hazard Type "(B))+EAL_("Hazard Type "(A))E A L_{\text {Hazard Type }}=E A L_{\text {Hazard Type }(P)}+E A L_{\text {Hazard Type }(B)}+E A L_{\text {Hazard Type }(A)}
We add up the EAL values for 18 types of hazards to obtain the composite EAL value. 我们将 18 种危害的 EAL 值相加，得出综合 EAL 值。
EAL_("Composite ")=sum_(i=1)^(18)EAL_("Hazard Type ")E A L_{\text {Composite }}=\sum_{i=1}^{18} E A L_{\text {Hazard Type }}
In order to describe our process of calculating the value of EAL more clearly. We draw the flowchart Figure 2 below. 为了更清楚地描述我们计算 EAL 值的过程。我们绘制了下图 2 流程图。
Figure 2: Calculation procedure for EAL 图 2：EAL 的计算程序
A national ranking is computed for the composite EAL value of each community. The resulting values are then converted into national percentiles to produce an EAL score for each community. The EAL scores are very helpful for the risk calculation in the following text. 根据每个社区的 EAL 综合值计算出全国排名。然后将得出的数值转换成全国百分位数，得出每个社区的 EAL 分数。EAL 分数非常有助于下文中的风险计算。
{:[EAL Rank=Rank(EAL_("Composite "))],[EALScore=(EAL" Score "-Min(EAL" Score "))/(Max(EAL" Score ")-Min(EAL" Score "))xx100]:}\begin{gathered}
E A L \operatorname{Rank}=\operatorname{Rank}\left(E A L_{\text {Composite }}\right) \\
E A L S c o r e=\frac{E A L \text { Score }-\operatorname{Min}(E A L \text { Score })}{\operatorname{Max}(E A L \text { Score })-\operatorname{Min}(E A L \text { Score })} \times 100
\end{gathered}
4.2.2 Community Risk Factor (CRF) 4.2.2 社区风险因素（CRF）
To generate a Community Risk Factor CRF (CRF) value for a community, its Social Vulnerability (SV) value is divided by its Community Resilience (CR) value. 要生成一个社区的社区风险因子 CRF 值，需要用其社会脆弱性 (SV) 值除以社区恢复力 (CR) 值。
CRF=f((SV)/(CR))C R F=f\left(\frac{S V}{C R}\right)
where f((SV)/(CR))f\left(\frac{S V}{C R}\right) is a triangular distribution with minimum 0.5 , maximum 2 , and mode 1 . 其中 f((SV)/(CR))f\left(\frac{S V}{C R}\right) 是一个三角形分布，最小值为 0.5，最大值为 2，模式为 1。
The selection process for the CRF involved evaluating various shapes, ranges, and modes. Considering its ability to highlight communities at both ends of the distribution without attributing extreme values to a select few, we use the triangular distribution. It also takes into account the EAL as the primary driver of risk, thereby making a mode of 1 the most appropriate choice for the CRF. CRF 的选择过程包括评估各种形状、范围和模式。考虑到三角形分布能够突出分布两端的群体，而不会将极端值归因于少数人，我们采用了三角形分布。它还考虑到了作为风险主要驱动因素的 EAL，从而使 1 模式成为 CRF 的最合适选择。
The SV values correspond to SOVI values, while the CR values represent HVRI BRIC index for the community, as provided by the source data sets. SV 值对应 SOVI 值，而 CR 值代表源数据集提供的 HVRI BRIC 社区指数。
4.2.3 Risk Calculation 4.2.3 风险计算
In the most general terms, natural hazard risk is often defined as the likelihood (or probability) of a natural hazard event happening multiplied by the expected consequence if a natural hazard event occurs. 最一般而言，自然灾害风险通常被定义为自然灾害事件发生的可能性（或概率）乘以自然灾害事件发生时的预期后果。
To make the level of risk more concrete and exemplified, we estimate risk from two aspects: risk value and risk score. 为了使风险水平更加具体化和例证化，我们从两个方面来估算风险：风险值和风险分值。
{:[R_("value ")=EAL_("value ")xx CRF],[R_("score ")=EAL_("score ")xx CRF]:}\begin{aligned}
& R_{\text {value }}=E A L_{\text {value }} \times C R F \\
& R_{\text {score }}=E A L_{\text {score }} \times C R F
\end{aligned}
where RR represents Risk. 其中 RR 代表风险。
This risk equation of RR includes three components: a natural hazards risk component, a consequence enhancing component, and a consequence reduction component. EAL is the natural hazards risk component, measuring the expected loss of building value, population, and/or agriculture value each year due to natural hazards. CRF incorporates both the consequence enhancing component, denoted as SV, and the consequence reduction component, represented by CR. RR 的风险等式包括三个部分：自然灾害风险部分、后果增强部分和后果减轻部分。EAL 是自然灾害风险部分，衡量每年因自然灾害造成的建筑物价值、人口和/或农业价值的预期损失。CRF 包含增强后果部分（以 SV 表示）和减少后果部分（以 CR 表示）。
For equation (8), values for Risk and EAL are in units of dollars, representing the community’s average economic loss from natural hazards each year. For SV and CR, values are the index values for the community provided by the source data sets. 对于公式 (8)，Risk 和 EAL 的值以美元为单位，代表社区每年因自然灾害造成的平均经济损失。对于 SV 和 CR，数值是源数据集提供的社区指数值。
For equation (9), each component is represented by a score that represents a community’s percentile ranking relative to all other communities at the same level. The composite risk score is calculated to measure a community’s risk to all 18 hazard types. And it is also a community’s percentile ranking in risk compared to all other communities at the same level. The risk score and EAL score are provided as both composite scores from the summation of all 18 hazard types. 对于公式 (9)，每个组成部分都用一个分值来表示，该分值代表一个社区相对于同一级别的所有其他社区的百分位数排名。计算综合风险分值是为了衡量一个社区在所有 18 种危害类型中的风险。它也是一个社区与同级别所有其他社区相比的风险百分位数排名。风险分数和 EAL 分数都是由所有 18 种危害类型的总和得出的综合分数。
We used the K-algorithm to categorize the disaster levels into five classes, as shown in Figure 3. 如图 3 所示，我们使用 K 算法将灾害等级划分为五个等级。
Figure 3: Risk rating and map presentation 图 3：风险评级和地图展示
4.3 Insurance Premium 4.3 保险费
Generally, the companies adopt the principle of Level Premium to determine the price of insurance. The company calculate the pure premium by using a pre-determined claim rate and a desired return on investment. The total premium is then obtained by adding surcharges at a certain expense ratio. Then, the total premium is obtained by adding surcharges at a certain expense ratio. Insurance companies increase their profitability by increasing expense ratios and reducing expected returns on investment. In addition, they utilize the ‘Law of Large Numbers’ to set the overall payout ratio of the product so that it basically matches the statistical data, thus reducing the company’s exposure to the risk of fluctuating payout ratios. For catastrophe insurance pricing, a natural disaster can cause huge property damage when it occurs. The insurance company may have a risk of becoming insolvent. 一般来说，公司采用 "水平保费 "原则来确定保险价格。公司通过预先确定的索赔率和期望的投资回报率来计算纯保费。然后，再按一定的费用率加上附加费用，得出总保费。然后，再按一定的费用比率加上附加费用，得出总保费。保险公司通过提高费用率和降低预期投资回报率来提高盈利能力。此外，他们还利用 "大数法则 "来设定产品的总体赔付率，使其与统计数据基本吻合，从而降低公司面临的赔付率波动风险。就巨灾保险定价而言，自然灾害发生时会造成巨大的财产损失。保险公司可能有破产的风险。
In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio. 在金融学中，资本资产定价模型（CAPM）是一个用于确定理论上适当的资产必要收益率的模型，以做出将资产加入分散投资组合的决策。
The reward-to-risk ratio for any individual security in the market is equal to the market reward-to-risk ratio, thus 市场上任何单个证券的收益风险比都等于市场收益风险比，因此
{:[(E(r_(i))-r_(f))/(beta_(i))=E(r_(m))-r_(f)],[beta_(i)=(Cov(R_(i),R_(m)))/(Var(R_(m)))=rho(i","m)(sigma_(i))/(sigma_(m))]:}\begin{array}{r}
\frac{E\left(r_{i}\right)-r_{f}}{\beta_{i}}=E\left(r_{m}\right)-r_{f} \\
\beta_{i}=\frac{\operatorname{Cov}\left(R_{i}, R_{m}\right)}{\operatorname{Var}\left(R_{m}\right)}=\rho(i, m) \frac{\sigma_{i}}{\sigma_{m}}
\end{array}
where 其中
E(r_(i))E\left(r_{i}\right) is the expected return on the capital asset, E(r_(i))E\left(r_{i}\right) 是资本资产的预期收益、
E(r_(m))E\left(r_{m}\right) is the expected return of the market, E(r_(m))E\left(r_{m}\right) 是市场的预期收益、
r_(f)r_{f} is the risk-free rate of interest such as interest arising from government bonds, r_(f)r_{f} 是无风险利率，如政府债券产生的利息、
beta_(i)\beta_{i} is the sensitivity of the expected excess asset returns to the expected excess mar- beta_(i)\beta_{i} 是预期超额资产回报对预期超额市场回报的敏感度。
ket returns, ket 返回、
rho(i,m)\rho(i, m) denotes the correlation coefficient between the investment ii and the market mm, rho(i,m)\rho(i, m) 表示投资 ii 与市场 mm 之间的相关系数、
sigma_(i)\sigma_{i} is the standard deviation for the investment ii, sigma_(i)\sigma_{i} 是投资 ii 的标准偏差、
sigma_(m)\sigma_{m} is the standard deviation for the investment mm. sigma_(m)\sigma_{m} 是投资 mm 的标准偏差。
Expected return on investment (ROI): 预期投资回报率 (ROI)：
ROI=int(-A xx l(p)+(1+x)A xxR_("value ")-I)/(I)f(p)dpR O I=\int \frac{-A \times l(p)+(1+x) A \times R_{\text {value }}-I}{I} f(p) d p
Variance of ROI: 投资回报率的差异：
Var(ROI)=int[(-A xx l(p)+A(1+x)xxR_("value ")-l-(Ax xxR_("value ")-l))/(I)]^(2)f(p)dp\operatorname{Var}(R O I)=\int\left[\frac{-A \times l(p)+A(1+x) \times R_{\text {value }}-l-\left(A x \times R_{\text {value }}-l\right)}{I}\right]^{2} f(p) d p
where 其中
AA is the sum insured, AA 为保险金额、
II is the invested capital, II 是投资资本、
l(p)l(p) is the loss function, l(p)l(p) 是损失函数、
xx is the surcharge rate. xx 是附加费率。
The surcharge rate xx is a multiple of the average value of the loss: 附加费率 xx 是损失平均值的倍数：
where sigma\sigma is the Standard deviation of R_("value ")R_{\text {value }}. 其中， sigma\sigma 是 R_("value ")R_{\text {value }} 的标准偏差。
Pure premium per $10,000 y\$ 10,000 y : 每 $10,000 y\$ 10,000 y 纯溢价：
y=10000(1+x)xx Py=10000(1+x) \times P
where PP is the probability of a disaster causing damage. 其中， PP 是灾害造成损失的概率。
Typically, it is more reasonable to spend 3-10 percent of each person’s annual income on insurance. We assume that each person is willing to spend 5%5 \% of his or her annual income each year to purchase catastrophe insurance with a one-year term. Insurance companies can make decisions from two perspectives based on the above formula: 通常情况下，将每个人年收入的 3%-10%用于购买保险更为合理。我们假设每人每年愿意花费其年收入的 5%5 \% 来购买为期一年的巨灾保险。保险公司可以根据上述公式从两个角度做出决策： >> Introducing bankruptcy theory, after calculating the lowest order price, y , in the case where the probability of the firm’s future bankruptcy is less than 10%10 \%, and then comparing it to the local per capita annual disposable income (GNI), it is expected that people in the locality will not be able to afford to consume catastrophe insurance and will not invest in it if the ratio of premiums per $10,000\$ 10,000 to GNI is greater than 5%5 \%. >> 引入破产理论，在计算出企业未来破产概率小于 10%10 \% 的情况下的最低订单价格y后，再与当地人均年可支配收入（GNI）进行比较，如果每 $10,000\$ 10,000 的保费与GNI之比大于 5%5 \% ，预计当地居民将无力消费巨灾保险，也不会投资巨灾保险。 >> We use 5%5 \% of the local national GNI per capita as the subscription price per $10,000\$ 10,000 of premium. If this price makes the likelihood of future insolvency of the company higher than 10%10 \%, no investment is made in that location. >> 我们用当地人均国民总收入的 5%5 \% 作为每 $10,000\$ 10,000 溢价的认购价格。如果该价格使公司未来破产的可能性高于 10%10 \% ，则不在该地投资。
The price of insurance also affects people’s desire to buy to some extent, and an increase in the price of insurance may lead to a decrease in their desire to buy. 保险价格也会在一定程度上影响人们的购买欲望，保险价格的上涨可能会导致人们购买欲望的下降。
N=(1-omega y)N_(A)N=(1-\omega y) N_{A}
" Total Revenue "=y xx N\text { Total Revenue }=y \times N
where 其中
N_(A)N_{A} is the total local population, N_(A)N_{A} 为当地总人口、
NN is the number of local people with a strong desire to buy, NN 是指当地有强烈购买欲望的人数、
omega\omega is the factor that influences the price of insurance on the willingness of locals to buy, and is related to the average disposable income of locals as well as the gap between the rich and the poor, omega\omega 是影响当地人购买意愿的保险价格因素，与当地人的平均可支配收入以及贫富差距有关、
Total Revenue is the projected total local insurance revenue. 总收入是预计的地方保险总收入。
The company first determines the area in which it wants to invest money to build the insurance and then determines the price of local insurance. We would like to maximize the company’s total revenue: 公司首先确定要在哪个地区投入资金建立保险，然后确定当地保险的价格。我们希望公司的总收入最大化：
{:[ max" Total Revenue "],[" s.t. "{[0 < omega y < 1],[y >= y_(10)],[y <= 0.05 xx GNI]:}]:}\begin{aligned}
& \max \text { Total Revenue } \\
& \text { s.t. }\left\{\begin{array}{l}
0<\omega y<1 \\
y \geqslant y_{10} \\
y \leqslant 0.05 \times G N I
\end{array}\right.
\end{aligned}
where y_(10)y_{10} is the price of insurance when the firm’s insolvency rate is 10 percent. 其中， y_(10)y_{10} 是公司破产率为 10% 时的保险价格。
Our model is implemented in Gorontalo, Indonesia and Los Angeles, California. This is because both locations have similar and high risk indices, with Los Angeles having the highest disaster risk index in the United States. 我们的模型在印度尼西亚戈伦塔洛和加利福尼亚州洛杉矶实施。这是因为这两个地方的风险指数相似且较高，其中洛杉矶的灾害风险指数是美国最高的。
Figure 4: Location of the two areas on the map 图 4：地图上两个区域的位置
After searching for relevant data, we calculated that in order to ensure that the probability of the company’s bankruptcy after investing in catastrophe insurance in Gorontalo is less than 10%10 \%, we need to charge a premium of $342.745\$ 342.745 for every $10,000\$ 10,000 of coverage, which is calculated in equation (14), of which $283.465\$ 283.465 is the pure premium and $59.28\$ 59.28 is the additional premium. Searching for relevant information we find that 5%5 \% of the per capita disposable in- 经过查找相关资料，我们计算出，为了确保戈龙塔洛省投资巨灾保险后公司破产的概率小于 10%10 \% ，我们需要为每 $10,000\$ 10,000 的保额收取 $342.745\$ 342.745 的保费，计算公式（14）为其中 $283.465\$ 283.465 为纯保费， $59.28\$ 59.28 为附加保费。通过搜索相关信息，我们发现人均可支配收入中的 5%5 \%
come (GNI) of Gorontalo is only $137.25\$ 137.25, so the likelihood of residents being willing to purchase catastrophe insurance is low and the company should not invest in catastrophe insurance in the area. 戈伦塔洛的国民总收入（GNI）只有 $137.25\$ 137.25 ，因此居民愿意购买巨灾保险的可能性很低，公司不应该在该地区投资巨灾保险。
In order to ensure that the probability of insolvency of the company after investing in catastrophe insurance in Los Angeles is less than 10%10 \%, through the formula (14) calculated that for every $10,000\$ 10,000 of coverage need to charge a premium of $295.09\$ 295.09 of which the pure premium is $200\$ 200 and the additional premium is $95.09\$ 95.09 (because of the higher return on investment in the market in the U.S.). The per capita disposable income in Los Angeles (5% of GNI is $3,162.65\$ 3,162.65 ), which is much higher than the cost of catastrophe insurance. In order to determine the most appropriate cost of insurance to earn a greater benefit, we plotted the trend of total premium income as a function of premiums. 为了保证公司在洛杉矶投资巨灾保险后的破产概率小于 10%10 \% ，通过公式（14）计算出每 $10,000\$ 10,000 的保额需要收取 $295.09\$ 295.09 的保费，其中纯保费为 $200\$ 200 ，附加保费为 $95.09\$ 95.09 （因为美国市场投资回报率较高）。洛杉矶的人均可支配收入（国民总收入的 5%为 $3,162.65\$ 3,162.65 ），远高于巨灾保险的成本。为了确定最合适的保险成本以获得更大的收益，我们绘制了总保费收入与保费的函数关系图。
Figure 5: Relationship between company revenue and insurance price in Los Angeles 图 5：洛杉矶公司收入与保险价格之间的关系
From the Figure 5, it can be seen that with the increase of premiums, the total income of insurance companies tends to increase first and then decrease. This is because when the premium is too low, although the number of insured people is high, the amount of single transaction is small and the number of guarantees is too high, which leads to a higher risk of bankruptcy of the insurance company; whereas too high a premium will reduce the consumer’s expectations of catastrophe insurance, and the volume of insurance orders will be small. 从图 5 可以看出，随着保费的增加，保险公司的总收入呈先增加后减少的趋势。这是因为保费过低时，虽然投保人数多，但单笔交易金额小，担保次数过多，导致保险公司破产风险较大；而保费过高，则会降低消费者对巨灾保险的预期，保险订单量小。
In summary, for Los Angeles, a premium of about 2,500 per $10,000\$ 10,000 of coverage can be used, and 1.92 million people are expected to purchase the company’s catastrophe insurance (the total population of Los Angeles is about 3.79 million). At this point, the insurance company’s theoretical revenue would be around $4.5\$ 4.5 billion. Although Los Angeles has a high risk index, the profits are equally attractive, so the insurance company could take the risk of launching its catastrophe insurance business here. 总之，就洛杉矶而言，每份 $10,000\$ 10,000 保险的保费约为 2,500 美元，预计将有 192 万人购买该公司的巨灾保险（洛杉矶总人口约为 379 万）。此时，保险公司的理论收入将在 $4.5\$ 4.5 亿左右。虽然洛杉矶的风险指数较高，但利润同样诱人，因此保险公司可以冒险在这里开展巨灾保险业务。
4.4 Measures 4.4 措施
4.4.1 Insurance Securitization 4.4.1 保险证券化
Catastrophe bonds are risk-linked securities that transfer a specified set of risks from a sponsor to investors. Catastrophe bonds emerged from a need by insurance companies to alleviate some of the risks they would face if a major catastrophe occurred, which would incur damages that they could not cover by the invested premiums. An insurance company issues bonds through an investment bank, which are then sold to investors. These bonds are inherently risky, and usually have maturities less than 3 years. If no catastrophe occurred, the insurance company would pay a coupon to the investors. But if a catastrophe did occur, then the principal would be forgiven and the insurance company would use this money to pay their claim-holders. 巨灾债券是一种与风险挂钩的证券，它将特定的风险从发起人转移给投资者。巨灾债券的出现源于保险公司的一种需求，即在发生重大巨灾时，保险公司需要减轻其所面临的一些风险，因为巨灾所造成的损失是保险公司投入的保费所无法弥补的。保险公司通过投资银行发行债券，然后出售给投资者。这些债券本身就有风险，期限通常少于 3 年。如果没有灾难发生，保险公司将向投资者支付票息。但如果发生了灾难，那么本金将被免除，保险公司将用这笔钱支付给索赔人。
Figure 6: Insurance securitization schema 图 6：保险证券化模式
From an economic perspective, the securitization of insurance, particularly through instruments like catastrophe bonds, represents a significant innovation in the capital markets. This innovation not only diversifies investment opportunities but also plays a crucial role in enhancing the resilience of the insurance industry against catastrophic events. Catastrophe bonds allow insurance companies to transfer the risk of extreme events, such as natural disasters, to the capital markets, thereby reducing their potential liability and improving their solvency. This mechanism enables insurance firms to manage their risk exposure more effectively and to maintain stability in the face of potentially ruinous events. By doing so, it also ensures that insurance companies can continue to offer coverage for risks that might otherwise be uninsurable due to their catastrophic potential. 从经济角度看，保险证券化，特别是通过巨灾债券等工具进行的证券化，是资本市场的一项重大创新。这一创新不仅使投资机会多样化，而且在增强保险业抵御巨灾事件的能力方面发挥着至关重要的作用。巨灾债券允许保险公司将自然灾害等极端事件的风险转移到资本市场，从而降低其潜在责任，提高偿付能力。这一机制使保险公司能够更有效地管理其风险敞口，并在面对潜在的破坏性事件时保持稳定。这样做还能确保保险公司能够继续承保因可能造成灾难而无法承保的风险。
4.4.2 Co-operation with the Government 4.4.2 与政府合作
The government plays an important role in the country. The government can make some appealing policies to stimulate people to buy insurance and cooperate with insurance companies to undertake part of the risk. When people buy insurance, individuals are only required to 政府在国家中扮演着重要角色。政府可以制定一些有吸引力的政策来刺激人们购买保险，并与保险公司合作承担部分风险。当人们购买保险时，个人只需
bear part of the premium. The remainder is subsidized by the various levels of government. If necessary, special groups of people may be fully covered by government finances. When a catastrophe occurs, the government can act as a reinsurer and bear part of the amount of compensation. If the amount of compensation is small, the insurance company will pay directly. Otherwise, it can be covered or partially paid by the government. In this way, a multi-layered diversification of risk is constructed. It not only brings benefit protection to the people, but also drives the development of the insurance industry. 承担部分保费。其余部分由各级政府补贴。必要时，特殊人群可由政府财政全额承担。当灾难发生时，政府可以作为再保险人，承担部分赔偿金额。如果赔偿金额较小，则由保险公司直接赔付。否则，可由政府承担或部分承担。通过这种方式，构建了多层次的风险分散机制。这不仅给老百姓带来了利益保障，也带动了保险业的发展。
4.4.3 The Implementation of Measures 4.4.3 措施的实施
Through the two scenarios described above, the insurance company’s market return on investment in the Gorontalo region r_(m)r_{m} increased. When a natural disaster occurs, the amount of compensation paid by the insurance company is shared by the insurance company, the investors in the insurance securities, and the local government. In addition, the government subsidizes residents for catastrophe insurance, which increases the willingness of residents to purchase catastrophe insurance and reduces the actual cost paid by individuals. The insurance company can set premiums at the lowest premium ($295.09) that can be assumed under the risk of insolvency. We plot the trend of total premium income as a function of premium at this point in time. 通过上述两种情况，保险公司在戈伦塔洛地区的市场投资回报 r_(m)r_{m} 增加了。自然灾害发生时，保险公司支付的赔偿金额由保险公司、保险证券投资者和当地政府共同承担。此外，政府对居民进行巨灾保险补贴，增加了居民购买巨灾保险的意愿，降低了个人实际支付的费用。保险公司可将保费定在破产风险下可承担的最低保费（295.09 美元）。我们将总保费收入的趋势绘制成保费在这一时点的函数。
Figure 7: The Analog trend of total premium income in Gorontalo 图 7：戈龙塔罗省总保费收入的模拟趋势
As we can see from the picture. Under the company’s affordable insolvency risk, the insurer expects maximum revenues of $245\$ 245 million. The company expects maximum revenue is $245\$ 245 million. At this time ,each $10,000\$ 10,000 of insurance amount charges $295.09\$ 295.09 of insurance premiums. We expect 830,255 people (about 73.26%73.26 \% of the total population) to have catastrophic insurance. Gorontalo residents pay only $137.25\$ 137.25 individually, and the remainder is subsidized by the Gorontalo government. The government guarantees the legal rights of Gorontalo residents as well as their social welfare. 从图中我们可以看到。在公司可承受的破产风险下，保险公司预计最高收入为 $245\$ 245 万。公司预计最大收入为 $245\$ 245 百万。此时，每 $10,000\$ 10,000 个保险金额收取 $295.09\$ 295.09 个保险费。我们预计将有 830 255 人（约占总人口的 73.26%73.26 \% ）购买重大疾病保险。戈伦塔洛居民只需个人支付 $137.25\$ 137.25 ，其余部分由戈伦塔洛政府补贴。政府保障戈伦塔洛居民的合法权利及其社会福利。
4.5 Real Estate Decision Making 4.5 房地产决策
Our insurance model has a significant impact on the development decisions of real estate 我们的保险模式对房地产开发决策具有重大影响
developers. Based on the above model derivation, it can be learned that for areas with high natural disasters and low per capita income, if the insurance company is willing to underwrite policies, it will result in the high bankruptcy rate of the company not being able to realize profitability. Similarly, real estate developers will not choose the area for investment and development due to high risk and lack of demand. That is, any area with high R value and income (GNI) below a certain value is not recommended for real estate developers to invest in. In addition to this, such areas have the following risk factors: 开发者。根据上述模型推导可知，对于自然灾害频发、人均收入较低的地区，如果保险公司愿意承保，就会导致公司破产率高，无法实现盈利。同样，房地产开发商也会因为高风险和需求不足而不选择该地区进行投资和开发。也就是说，凡是 R 值高、收入（国民总收入）低于某一数值的地区，都不建议房地产开发商投资。除此之外，这类地区还存在以下风险因素：
Figure 8: Risk factors 图 8：风险因素
Further applying our model, we can calculate the insurance rate, which is the insurance premium divided by insurance amount. If the area has a high insurance rate by calculating, the property developer would have to bear a higher insurance cost during the construction of the building as well as during the unsold period. Therefore, property developers need to carefully consider and weigh the future profit and loss before making decisions. 进一步应用我们的模型，我们可以计算出保险费率，即保险费除以保险金额。如果通过计算得出该地区的保险费率较高，那么房地产开发商在建筑施工期间和未售出期间就必须承担较高的保险费用。因此，房地产开发商在做出决定之前，需要仔细考虑和权衡未来的盈亏。
Similarly, in other areas, we can calculate local insurance rates based on our model. According to this indicator, property developer can further determine the cost of developing land in local area and buying insurance. In this way we provide a reference for the property developer’s decision making. 同样，在其他地区，我们可以根据模型计算当地的保险费率。根据这一指标，房地产开发商可以进一步确定在当地开发土地和购买保险的成本。这样，我们就为房地产开发商的决策提供了参考。
Additionally, our model can also provide guidance about how property developers build construction. For each of the 18 hazard types, we can calculate the value of EAL and R_("value ")R_{\text {value }} (in dollars) for each hazard type. We find a positive correlation between EAL and R_("value ")R_{\text {value }} to some extent. Thus, property developers can determine the different major hazrard type for each area based on R_("value ")\mathrm{R}_{\text {value }} and thus build different types of homes. For example, in the city of New Orleans, USA, flooding ranks high on the list of 18 natural disasters in terms of R_("value ")\mathrm{R}_{\text {value }}. Accordingly, many property companies, such as American Restorators LLC, are building houses with high foundations locally to minimize damage and achieve business profitability. Our model solves the problem about how to build on certain site. This approach not only maintains the interests of real property developers, but also protects the lives of people in the community. 此外，我们的模型还可以为房地产开发商如何建造建筑提供指导。对于 18 种危险类型中的每一种，我们都可以计算出每种危险类型的 EAL 值和 R_("value ")R_{\text {value }} （单位：美元）。我们发现 EAL 与 R_("value ")R_{\text {value }} 在一定程度上呈正相关。因此，房地产开发商可以根据 R_("value ")\mathrm{R}_{\text {value }} 确定每个地区的不同主要危险类型，从而建造不同类型的住宅。例如，在美国新奥尔良市，洪水在 R_("value ")\mathrm{R}_{\text {value }} 的 18 种自然灾害中名列前茅。因此，许多房地产公司（如 American Restorators LLC）都在当地建造地基较高的房屋，以尽量减少损失，实现业务盈利。我们的模式解决了如何在特定地点建造房屋的问题。这种方法不仅维护了房地产开发商的利益，也保护了社区居民的生命安全。
5 Building Preservation Model 5 建筑保护模式
5.1 Building Value Quantification 5.1 建筑价值量化
Building value is measured in terms of the building’s cultural value and community influence, economic value, and historical value. Therefore, we take these three main aspects as primary indicators. 建筑价值的衡量标准包括建筑的文化价值和社区影响力、经济价值和历史价值。因此，我们将这三大方面作为主要指标。
5.1.1 Indicators Determination 5.1.1 指标的确定
For the cultural value and community influence, we synthesized various factors, such as geography and network, and finally selected the three most representative secondary indicators to construct our model. Similarly, for the economic and historical value, we selected two secondary indicators each to improve the model. The specific description and indicators selected are shown in Table 3. 在文化价值和社区影响力方面，我们综合了地理、网络等多种因素，最终选择了三个最具代表性的二级指标来构建模型。同样，对于经济价值和历史价值，我们也分别选取了两个二级指标来完善模型。具体描述和所选指标如表 3 所示。
Table 3: Indicators 表 3：指标
Object 对象
Indicators 指标
Description 说明
文化价值观和
社区影响力
Cultural Values and
Community influence
Cultural Values and
Community influence| Cultural Values and |
| :---: |
| Community influence |
NG
Number of Google search terms 谷歌搜索词数量
P
参与活动
在大楼周围举行
Participation in events
held around the building
Participation in events
held around the building| Participation in events |
| :---: |
| held around the building |
ANV
Annual number of visitors 每年游客人数
Economy 经济
LV
Land value 土地价值
CC
Construction cost 建筑成本
History 历史
NH
Number of historical research documents 历史研究文件的数量
DP
Degree of preservation 保存程度
Object Indicators Description
"Cultural Values and
Community influence" NG Number of Google search terms
P "Participation in events
held around the building"
ANV Annual number of visitors
Economy LV Land value
CC Construction cost
History NH Number of historical research documents
DP Degree of preservation| Object | Indicators | Description |
| :---: | :---: | :---: |
| Cultural Values and <br> Community influence | NG | Number of Google search terms |
| | P | Participation in events <br> held around the building |
| | ANV | Annual number of visitors |
| Economy | LV | Land value |
| | CC | Construction cost |
| History | NH | Number of historical research documents |
| | DP | Degree of preservation |
Cultural Value and Community Influence 文化价值和社区影响
Global Visibility 全球知名度
The cultural value of a building depends to a large extent on its global visibility. So we quantify its global visibility through two metrics, ‘Number of Google search terms’ (NG) and ‘Annual number of visitors’ (ANV). This approach balances online and offline, making the measurement of cultural values more quantifiable and accurate. 一座建筑的文化价值在很大程度上取决于其全球知名度。因此，我们通过 "谷歌搜索词数量"（NG）和 "年访问人数"（ANV）这两个指标来量化其全球知名度。这种方法兼顾了线上和线下，使文化价值的衡量更加量化和准确。
Impact on the Community 对社区的影响
Buildings have a strong connection with local communities. When measuring the value of a building, we take into account its impact on the local community. Research has shown that the more influence a building has on the local community, the more the value of the landmark itself will increase. Besides, it will further promote the increase of influence, realizing a positive feedback loop. Therefore, we choose ‘Participation in events held around the building’ § to quantify the building’s influence on the community. We calculate P as follows: 建筑物与当地社区有着密切的联系。在衡量建筑物的价值时，我们会考虑其对当地社区的影响。研究表明，建筑物对当地社区的影响越大，地标建筑本身的价值就会越高。此外，它还会进一步促进影响力的提升，实现正反馈循环。因此，我们选择 "参与建筑周边活动"§ 来量化建筑对社区的影响力。我们计算 P 的方法如下
P=(1)/(N)xxsum_(i=1)^(N)(NCMP_(i))/(NTC_(i))P=\frac{1}{N} \times \sum_{i=1}^{N} \frac{N C M P_{i}}{N T C_{i}}
where NCMP_(i)\mathrm{NCMP}_{i} represents ‘Number of community members participating in activities’ at the ii th activity, NTC_(i)\mathrm{NTC}_{i} means the total number of people in the community at the time of the ii th activity and N means the total number of activities conducted around the building. 其中， NCMP_(i)\mathrm{NCMP}_{i} 表示 ii 次活动时的 "参加活动的社区成员人数"， NTC_(i)\mathrm{NTC}_{i} 表示 ii 次活动时的社区总人数，N 表示围绕建筑物开展的活动总数。
- Economy Value - 经济价值
For economic value, we mainly consider the value of the building in terms of its construction. Therefore, we considered the value of the land it occupies. And it is measured by the indicator ‘Land value’ (LV). 就经济价值而言，我们主要考虑的是建筑物的建造价值。因此，我们考虑了其占用土地的价值。它由指标 "土地价值"（LV）来衡量。
LV=P_(c)xx" Area "L V=P_{c} \times \text { Area }
where P_(c)P_{c} represents the current price of the land and Area represents the area occupied by the building. Meanwhile, for the value created during the construction of the building itself, we use ‘Construction cost’ (CC) for quantitative assessment. Taking inflation into account, we define Construction cost as all costs involved in the implementation of that construction project under this year’s Engineering News-Record (ENR) benchmark for the region. Both the LVL V and CCC C metrics are expressed in U.S. dollars. 其中 P_(c)P_{c} 代表土地的当前价格，Area 代表建筑物所占面积。同时，对于建筑施工过程中创造的价值，我们使用 "建筑成本"（CC）进行量化评估。考虑到通货膨胀因素，我们将 "建筑成本 "定义为该地区本年度《工程新闻记录》（ENR）基准下实施该建筑项目所涉及的所有成本。 LVL V 和 CCC C 指标均以美元表示。
- Historic Value - 历史价值
Historical Research Value 历史研究价值
The historical value of a building is largely dependent on its place in historical research. So we quantify its visibility and importance in the academic world through NH.NH\mathrm{NH} . \mathrm{NH} refers to the number of historical research documents related to the building, including but not limited to books, papers, reports, etc. This indicator reflects the building’s attention and depth of research in the historical community. The higher NH value means the building has a higher historical research value. 一座建筑的历史价值在很大程度上取决于它在历史研究中的地位。因此，我们通过 NH.NH\mathrm{NH} . \mathrm{NH} 来量化其在学术界的知名度和重要性， NH.NH\mathrm{NH} . \mathrm{NH} 指的是与该建筑相关的历史研究文献的数量，包括但不限于书籍、论文、报告等。这一指标反映了该建筑在历史界的关注度和研究深度。NH 值越高，说明该建筑的历史研究价值越高。
The Preservation Condition 保存条件
The historic value of a building is also affected by its state of preservation. We use ‘Degree of preservation’ (DP) to measure the extent to which a building has been preserved from its original state. It includes aspects such as structural integrity, exterior preservation, and interior decoration. The assessment of DP can be based on expert review, preservation grade, and comparative analysis with the original state. Highly preserved buildings not only better transmit history and culture, but also provide rich materials for future research. 建筑的历史价值还受到其保存状况的影响。我们使用 "保存程度"（DP）来衡量建筑物在原有基础上的保存程度。它包括结构完整性、外部保护和内部装饰等方面。对 "保存程度 "的评估可基于专家审查、保存等级以及与原状的对比分析。保存完好的建筑不仅能更好地传承历史文化，还能为未来的研究提供丰富的素材。
5.1.2 Weight Calculation 5.1.2 重量计算
CRITIC is an objective assignment method based on data volatility. The idea of this method was based on two indicators, contrast intensity and correlation indicators. When calculating the weights, we need to multiply the contrast intensity with the correlation indicator and then normalize to get the final weights. CRITIC 是一种基于数据波动性的客观分配方法。这种方法的理念基于两个指标，即对比强度和相关性指标。在计算权重时，我们需要将对比强度与相关性指标相乘，然后进行归一化处理，得出最终权重。
Contrast intensity refers to the magnitude of the difference in values between evaluation programs for the same indicator, expressed as a standard deviation. The larger the standard deviation, the greater the fluctuation. That is, the larger the difference in the values taken between the programs, the higher the weight will be. 对比强度是指同一指标在不同评价方案之间的数值差异幅度，用标准差表示。标准差越大，波动就越大。也就是说，方案之间的取值差异越大，权重就越高。
The Sperman correlation coefficient is used to express the correlation between indicators. If there is a strong positive correlation between two indicators, it means that the less conflicting they are, the lower the weight will be. 斯佩尔曼相关系数用于表示指标之间的相关性。如果两个指标之间存在很强的正相关性，就意味着它们之间的冲突越小，权重就越低。
There are nn samples to be evaluated and pp evaluation indicators to form the raw indicator data matrix. 有 nn 个待评估样本和 pp 个评估指标组成原始指标数据矩阵。
where x_(ij)x_{i j} represents the value of the jj th evaluation indicator for the ii th sample. 其中， x_(ij)x_{i j} 表示 jj 第三个评价指标在 ii 第三个样本中的值。
2) In order to remove the effect of the scale each indicator is normalized. The indicators we selected are of benefit attributes type, so the normalization formula: 2) 为了消除比例尺的影响，对每个指标进行归一化处理。我们选择的指标属于效益属性类型，因此归一化公式为
where X_(ij)X_{i j} is normalized to obtain a numerical matrix. 其中 X_(ij)X_{i j} 经过归一化处理，得到一个数值矩阵。
3) Then we calculate the contrast intensity of the indicator: 3) 然后计算指标的对比强度：
where S_(j)S_{j} represents the strength of comparison of the jj th indicator. 其中， S_(j)S_{j} 表示第 jj 个指标的比较强度。
The larger the S_(j)S_{j}, the greater the difference in values for that indicator. The more information the indicator reflects, the stronger the evaluation strength of the indicator itself and the more weight should be assigned to it. S_(j)S_{j} 越大，该指标值的差异就越大。指标反映的信息越多，指标本身的评价力度就越强，权重也就越大。
4) Calculation of the conflicting nature of the indicators 4) 计算指标的冲突性
where r_(jk)r_{j k} denotes the Sperman correlation coefficient between evaluation indicators jj and kk. R_(j)R_{j} denotes the conflictual of the jj th indicator. 其中 r_(jk)r_{j k} 表示评价指标 jj 和 kk 之间的斯佩尔曼相关系数。 R_(j)R_{j} 表示第 jj 个指标的冲突性。
The Sperman correlation coefficient is used to express the correlation between indicators. The stronger the correlation between two indicators, the less they conflict, the more they reflect the same information, and the more repetitive the content of the evaluation is. To a certain extent, the evaluation strength of the indicator is weakened and the weight assigned to it should be reduced. 斯佩尔曼相关系数用于表示指标之间的相关性。两个指标之间的相关性越强，它们之间的冲突就越小，反映的信息就越相同，评价内容的重复性就越强。在一定程度上，该指标的评价力度会被削弱，应降低其权重。
5) Calculation of the amount of information: 5) 计算信息量：
C_(j)=S_(j)xxR_(j)C_{j}=S_{j} \times R_{j}
Based on the amount of information, we calculate the weights of each indicator defined w_(j)w_{j} : 根据信息量，我们计算出定义为 w_(j)w_{j} 的每个指标的权重：
where object represents ‘Cultural values and community influence’, ‘Economy’, ‘History’, s_(j)s_{j} denotes the value of the jj th secondary indicator. 其中，object 表示 "文化价值和社区影响"、"经济"、"历史"， s_(j)s_{j} 表示第 jj 个二级指标的值。
Applying the CRITIC weighting method for each level 1 indicator separately, the objective weights for each level 2 indicator were obtained as shown in the following Table 1. 对每个一级指标分别采用 CRITIC 权重法，得出每个二级指标的客观权重如下表 1 所示。
5.1.3 Quantitative Results of Building Values 5.1.3 建筑物价值的量化结果
In order to assign weights to these three level 1 indicators to get the final building value, we use hierarchical analysis to construct a judgment matrix to get the weights of the three level 1 indicators: 为了给这三个一级指标分配权重，以获得最终的建筑价值，我们使用层次分析法构建了一个判断矩阵，以获得三个一级指标的权重：
5.2 Determination of protection measures 5.2 确定保护措施
5.2.1 Measure Score 5.2.1 衡量得分
In Model 1, we obtained a composite risk score R_("score ")R_{\text {score }} of each region by analyzing 18 natural hazards. Next, in the above section, we quantified the value of the building to get the score V_("score ")V_{\text {score }}. By multiplying the risk score and the value score, M_("score ")M_{\text {score }} is obtained, which is used to assess the conservation priority of the building and the extent and scale of conservation measures that need to be taken. 在模型 1 中，我们通过分析 18 种自然灾害，得到了每个地区的综合风险得分 R_("score ")R_{\text {score }} 。接下来，在上一节中，我们对建筑物的价值进行了量化，得到了得分 V_("score ")V_{\text {score }} 。将风险分值和价值分值相乘，得到 M_("score ")M_{\text {score }} ，用于评估建筑物的保护优先级以及需要采取的保护措施的范围和规模。
A higher M_("score ")M_{\text {score }} indicates a higher value of the building, along with a higher risk of exposure to natural hazards. Therefore, more urgent and comprehensive protection measures are needed. Based on the statistical distribution of M_("score ")M_{\text {score }}, we set reasonable thresholds to recognize low, medium, and heigh grades, and the values of the specific thresholds need to be set based on expert recommendations and industry standards. M_("score ")M_{\text {score }} 越高，表明建筑物的价值越高，遭受自然灾害的风险也越高。因此，需要采取更紧急、更全面的保护措施。根据 M_("score ")M_{\text {score }} 的统计分布，我们设定了合理的阈值来识别低、中、高三个等级，具体阈值的值需要根据专家建议和行业标准来设定。
5.2.2 Score of Protection Measures 5.2.2 保护措施得分
Low: For low-grade M_("score ")M_{\text {score }} buildings, basic conservation measures, such as routine maintenance and inspections and, where necessary, minor repairs, are undertaken. The risk or value of these buildings is low, so the measures taken are mainly preventive and low-cost. 低：对于低等级的 M_("score ")M_{\text {score }} 建筑，采取基本的保护措施，如日常维护和检查，必要时进行小型修缮。这些建筑的风险或价值较低，因此采取的措施主要是预防性的、低成本的。
Medium: For medium-grade M_("score ")M_{\text {score }}, moderate protection measures are implemented, including enhanced structural inspections, improved safety features, and disaster preparedness programs. These measures aim to increase the resistance and resilience of buildings and require moderate investment. 中等：对于中等级 M_("score ")M_{\text {score }} ，实施中等保护措施，包括加强结构检查、改进安全设施和防灾计划。这些措施旨在提高建筑物的抵抗力和复原力，需要适度投资。
High: For high-grade M_("score ")M_{\text {score }}, implement comprehensive and high-intensity protection measures. This may include comprehensive structural reinforcement, installation of advanced security systems, and customized risk management plans in cooperation with external experts. Given the high risk or value of these buildings, the goal of the measures is to minimize potential losses, even if this means higher initial costs. 高：对于高等级 M_("score ")M_{\text {score }} ，实施全面和高强度的保护措施。这可能包括全面的结构加固、安装先进的安全系统，以及与外部专家合作定制风险管理计划。鉴于这些建筑的高风险或高价值，这些措施的目标是最大限度地减少潜在损失，即使这意味着更高的初始成本。
Note that: The “one-size-fits-all” approach to disaster protection measures ignores the impact of regional differences, architectural characteristics and socio-economic factors, and can lead to poor protection and resource utilization. So specific protection measures still need to be derived from a thoughtful local analysis by natural disaster experts. 请注意灾害防护措施 "一刀切 "的做法忽视了地区差异、建筑特点和社会经济因素的影响，可能导致防护不力和资源利用率低下。因此，具体的保护措施仍需要自然灾害专家在当地进行深思熟虑的分析后得出。
5.2.3 Mentoring for Community Leaders 5.2.3 对社区领袖的指导
Our model provides a quantitative and systematic framework for community leaders to help them determine the extent and priority of preservation measures based on a building’s risk 我们的模型为社区领导者提供了一个定量和系统的框架，帮助他们根据建筑物的风险确定保护措施的范围和优先顺序
