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大学生,数学建模,美国大学生数学建模竞赛,MCM/ICM,2024年美赛特等奖O奖论文
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Problem Chosen
E
2024
MCM/ICM
Summary Sheet
Team Control Number
2401102
In Face of Increasingly Severe Extreme Weather:
Sustainable Property Insurance under Risk
Summary
The rst priority of survival is getting protection from the extreme weather. —Bear Grylls
More frequent and severe extreme weather events are causing greater damage to people’s prop-
erty, leading to a reevaluation of the sustainability of insurance companies. On one hand, maintaining
enough customers for long-term healthy operation is crucial; on the other hand, avoiding excessively
high compensation risks to remain protable is essential. Therefore, we assessed the sustainability of
the insurance sector in areas that were frequently impacted by extreme weather events from two per-
spectives: insurance demand and total risk.
For Task 1, we developed a Property Insurance Posture Model for insurance companies. We
categorized extreme weather into 4 types and used an ARIMA model to forecast the future risk of
extreme weather for each region-disaster pair, and calculated the expected loss. Then, we used Lane’s
AFC model to calculate premiums. To measure demand with premiums, we introduced the insurance
demand curve. Finally, we established Demand-Risk Equilibrium Model for Insurance(DBMI) to
provide decisions on whether to underwrite insurance in specic regions.
Next, we applied the model above to Australia and Southeast Asia, where approximately 60 years of
data from 3000 records were available. Then we applied ARIMA model on selected area-event series,
with an eminent t: R
2
consistently above 0.625, and IC all below 300. Consequently, we forecast
the risks for 2024-2027. This has resulted in the determination of premiums ranging from $119.2 to
$1295.6. The optimal solutions indicated that in Australia, QLD and WA should be underwritten; in
SE Asia, PHL and THA.
For Task 2, we introduced Innovative Risk Prediction Property Development Method(IRPPDM),
which integrated DBMI with real estate companies’ willingness index to construct a Willingness-Risk
coordinate system. We specically targeted High Risk-High Willingness areas, providing 3 possible
risk reassessment methods to help transfer them into Low Risk-High Willingness category.
For Task 3, we used Historic Landmark Preservation Model to help community leaders. We
estimated the signicance of historic landmarks by AHP method considering 8 indicators in 4 dimen-
sions. Then we oered suggestions considering both the extent of signicance and predicted risks.
According to our model, Temple of Literature in Hanoi, Vietnam had a score of 0.463, facing risks
of oods and cyclones. Considering its features, we oered 4 tailored suggestions.
In the end, we stated the strengths and weaknesses of models. Based on their performances in
application, Property Insurance Posture Model reasonably balanced demand and risk, and Historic
Landmark Preservation Model was comprehensive in measuring value.
Keywords: Extreme Weather Event; Property Insurance; ARIMA; Dual-objective Optimization; AHP
Team # 2401102 Page 1 of 25
Contents
1 Introduction 2
1.1 Problem Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Our Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Assumptions and Notations 3
3 Model I: Property Insurance Posture Model 4
3.1 The Types of Extreme Weather Events . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.2 Predicting Extreme Weather Events: Based on ARIMA . . . . . . . . . . . . . . . . . 5
3.2.1 Series Stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.2.2 ARIMA Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.3 Insurance Price and Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.3.1 Two Types of Insurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.3.2 Price of Insurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.3.3 Demand for Insurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.4 Demand-Risk Equilibrium Model for Insurance . . . . . . . . . . . . . . . . . . . . . 9
4 Case Study: Australia and Southeast Asia 10
4.1 Data Processing and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.2 Use of ARIMA Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.3 Apply DEMI to Two Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.3.1 Determination of Premiums and Demand . . . . . . . . . . . . . . . . . . . . 13
4.3.2 Solving DBMI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
5 Innovative Risk Prediction Property Development Method 14
5.1 Whether to Build: Determined by Willingness and Risk . . . . . . . . . . . . . . . . . 15
5.2 How and Where to build: Addressing Specic Event Risk . . . . . . . . . . . . . . . . 16
5.3 Conclusion for IRPPDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
6 Model II: Historic Landmark Preservation Model 17
6.1 Indicator Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
6.2 Weight Calculation: Based on AHP . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
6.3 Value Calculation and Extent Estimation . . . . . . . . . . . . . . . . . . . . . . . . . 20
6.4 Application: Temple of Literature in Hanoi, Vietnam . . . . . . . . . . . . . . . . . . 21
7 Strength and Weakness 22
References 23
Letter of Recommendation 24
Team # 2401102 Page 2 of 25
1 Introduction
1.1 Problem Background
Over the past few years, more than 1,000 extreme weather events have resulted in more than $1 trillion in
global losses. Swiss Re predicted that losses from weather-related events in Australia, Canada, France,
Germany, Japan, the U.K., and the U.S. could increase by 35-120 percent by 2040, due to the impact
of natural disasters such as oods, hurricanes, and wildres. [1]
Figure 1: Global Impact of Natural Disasters[2]
The frequent occurrence of extreme weather events presents a complex challenge for the property
insurance industry. These events can lead to substantial nancial losses due to increased claims, testing
the industry’s resilience. Insurers must navigate the dual pressures of maintaining protability and
oering aordable premiums.
Therefore, there’s a growing need for risk assessment models that accurately reect the high level
risks associated with extreme weather events. This will help insurers to price policies more eectively
and encourage investment in protective measures for properties at risk.
1.2 Our Work
For insurance companies, we have developed a property insurance deployment model to assist them
in selecting the areas to underwrite against extreme weather events, ensuring the sustainability of their
operations. Specically, we measured sustainability based on the company’s total demand and the total
risk they face: Demand reected the consideration of protability, while underwriting risk was related
to long-term healthy operation. After the model was established, we applied it to two dierent regions
to validate its feasibility.
For real estate developers, we extended the insurance model mentioned above to assist in the
decision-making process for property development, providing insights on where, how, and whether
Team # 2401102 Page 3 of 25
to construct buildings. Specically, using the weather risk predictions obtained from the insurance
model, we provided corresponding strategies that developers could implement to mitigate risks during
the construction of properties.
For community leaders without the shelter of extreme weather event insurance, we have developed
a historical landmark signicance model that assesses the signicance of historical landmarks based
on four aspects: history, culture, economy, and community. Ultimately, this helps them determine the
extent of protection needed for their historical landmarks.
The detailed owchart is illustrated in Figure 2 below:
Figure 2: Flowchart
2 Assumptions and Notations
Assumption1: Insurance companies bear the risk independently
Justication: In reality, insurance companies often diversify risks through nancial products, govern-
ment support, and other means. Since we focus on the design of insurance products, we assume that
insurance companies do not adopt risk diversication measures.
Team # 2401102 Page 4 of 25
Assumption2: Insurance demand is negatively correlated with price, and insurance demand re-
ects the number of customers.
Justication: Insurance, as a normal good, experiences a decrease in demand as its price increases.
And insurance demand corresponds to the number of insurance policies, and it can be directly seen as
reecting the number of customers.
Assumption3: Existing real estate development processes do not primarily consider extreme
weather risk predictions.
Justication: Extreme weather events have low frequencies and high randomness, making them dif-
cult to predict. Additionally, we conducted keyword searches on Google Scholar, and there is little
discussion on incorporating extreme weather risk predictions into the primary indicators for real estate
development.
Assumption4: The data we use is true and reliable.
Justication: Our data sources include international statistical agencies, academic databases, and rep-
utable insurance companies. Therefore, we can condently state that the data we use is accurate and
reliable for modeling purposes.
Notations
Symbol Denition
EL Expected Loss
PEL Frequncy of Loss
Q Quantity of Insurance Demand
D Insurance Demand
R Total Risk for Insurance
Sustainability Sustainability for Insurance Company
DBMI Demand-Risk Equilibrium Model for Insurance
IRPPDM Innovative Risk Prediction Property Development Method
HLPM Historical Landmark Preservation Model
3 Model I: Property Insurance Posture Model
3.1 The Types of Extreme Weather Events
According to USDA Climate Hubs, extreme events are occurrences of unusually severe weather or
climate conditions that can cause devastating impacts on communities and agricultural and natural
ecosystems.
NASA provided a brief summary of global extreme weather events, including heat waves, wildres,
droughts, tropical cyclones, heavy precipitation, oods, high-tide ooding, and marine heat waves.[3]
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