Exercises for Chapter 1#
Exercise 1.1 2023 Global and Thailand Top Finance and Economic Stories
Objective:
This exercise aims to develop your skills in summarizing and citing important finance and economic events from both global and Thailand contexts in the year 2023. The emphasis on proper referencing encourages good research practices and ensures the credibility of your findings.
Instructions:
Look up the internet to find and choose the top three stories about Finance and Economy in 2023 for both the global or Thailand perspectives.
Summarize each story in simple words, emphasizing key events and their impact on the global and Thai economies.
Include appropriate references and citations for each story. Failure to do so will result in a 50% deduction of total marks.
Submit your results on the Google Form, the link for which will be provided in class.
Exercise 1.2 Group Reading Project: Exploring the Historical Evolution of Actuarial Science
Objectives: In the exercise section, we will focus on hands-on activities and materials related to the historical development of actuarial science. These practical tasks will help you apply what you’ve learned and gain a better understanding of how actuarial science has evolved.
Group Size: Up to 4 students per group
Instructions:
Reading and Analysis: Read the materials carefully about the history of actuarial science. Look for important dates, people, and events that shaped its development.
Summarization: Work together to create a short summary highlighting the main points you found. Include key facts, notable figures, and any significant changes in actuarial science over time.
References: Don’t forget to mention where you got the information. Write down the titles, authors, or sources of the materials you used in your summary.
Submission: Submit your results on the Google Form, the link for which will be provided in class.
Exercise 1.3 Property/Casualty Insurance Pricing: Car Insurance
Objective
The goal is to estimate the premium for car insurance based on the given information about claim frequency, claim amount, and policy count.
Given Information
Claim Frequency (\(\lambda\)): 0.5 accidents per person per year.
Claim Amount (Claim Severity): 20,000 Baht per claim.
Policy Count (\(N\)): 100 policies in the portfolio.
Assumptions
The number of claims follows a Poisson distribution, which is a common assumption for modeling rare events like accidents.
Claim amounts are independent and identically distributed.
Calculation Process
1. Expected Claims per Policy
The Poisson distribution is used to model the number of claims.
\( \begin{align} \text{Expected Total Number of Claims} &= \text{Claim Frequency} \times \text{Policy Count} \\ &= 0.5 \times 100 = 50 \end{align} \)
2. Expected Total Cost
The expected total cost is calculated by multiplying the expected total number of claims by the average claim amount.
\( \begin{align} \text{Expected Total Cost} &= \text{Expected Total Number of Claims} \times \text{Claim Amount} \\ &= 50 \times 20,000 = 1,000,000 \, \text{Baht} \end{align} \)
3. Premium Calculation
The premium is then determined by dividing the expected total cost by the number of policies.
\( \begin{align} \text{Premium} &= \frac{\text{Expected Total Cost}}{\text{Policy Count}} \\ &= \frac{1,000,000}{100} = 10,000 \, \text{Baht} \end{align} \)
Conclusion
Based on the provided claim frequency, claim amount, and policy count, the estimated premium for car insurance is 10,000 Baht per person per year.
Exercise 1.4
In Exercise 1.3, we use the expected values to figure out how much insurance should cost, what problems or challenges do you think might come up?
Can you give an example to explain why relying only on expected values might not be enough?
Solution to Exercise 1.4
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When relying solely on expected values to determine insurance costs, several problems or challenges may arise. One significant limitation is that expected values provide only an average estimate and do not account for the variability and uncertainty inherent in insurance claims.
For example, consider a car insurance company using the average expected cost of claims to set premiums. If the company only considers the average cost per claim without accounting for the possibility of rare but costly accidents, it may underestimate the potential financial risk. In reality, there might be instances of high-cost claims due to severe accidents or legal disputes, which could significantly impact the insurer’s financial stability if not adequately accounted for.
Additionally, expected values may not reflect the full range of possible outcomes. Insurance claims can vary widely in frequency and severity, and relying solely on averages may overlook extreme events (tail events) with low probability but high impact. Ignoring these tail events can lead to underestimation of risk and inadequate pricing of insurance policies.
In summary, while expected values provide a useful starting point for insurance pricing, they have limitations in capturing the full spectrum of risks and uncertainties. A more comprehensive approach, such as incorporating probability distributions, is necessary to account for variability, tail events, and the probabilistic nature of insurance claims.
Exercise 1.5
When determining car insurance premiums, accidents don’t happen the same way for everyone, and their costs can vary. How could using a probability distribution help us capture the range of possible scenarios and their likelihood? Can you explain how considering probabilities might be more informative than just using a single average value when setting premiums?
Solution to Exercise 1.5
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Using a probability distribution in determining car insurance premiums allows us to capture the range of possible scenarios and their likelihood more effectively. Unlike relying on a single average value, which provides only a central estimate, a probability distribution accounts for the variability and uncertainty inherent in insurance claims.
For instance, consider a probability distribution representing the frequency and severity of car accidents. By examining the distribution, we can assess the likelihood of various outcomes, such as minor fender benders, moderate collisions, or severe accidents. Each outcome is associated with a probability, reflecting how often it is expected to occur.
This information is invaluable for insurance companies when setting premiums. Instead of basing premiums solely on the average expected cost of claims, which may not accurately represent the full spectrum of risks, insurers can use the probability distribution to account for different scenarios. For example, they can adjust premiums to reflect the likelihood of more frequent but less costly accidents versus rare but more expensive ones.
Considering probabilities provides a more informative and nuanced approach to setting premiums. It allows insurers to better assess the overall risk associated with insuring different drivers and vehicles. By incorporating probabilities, insurers can tailor premiums to specific risk profiles, ensuring that they adequately cover potential claims while remaining competitive in the market.
In summary, using a probability distribution in determining car insurance premiums enables insurers to capture the variability and uncertainty of accidents more comprehensively. It provides a more informative framework for assessing risk and setting premiums compared to relying solely on a single average value.