Chapter 2 Insurance and Risk
Fourteenth Edition, Global Edition
Lecturer: Jieyu Lin
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Definition of Insurance
• Insurance is the pooling of fortuitous losses by transfer
of such risks to insurers, who agree to indemnify insureds
for such losses, to provide other financial benefits on their
occurrence, or to render services connected with the risk
-- Commission on Insurance Terminology of the American Risk and
Insurance Association
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Basic Characteristics of Insurance (1 of 4)
• An insurance plan or arrangement typically includes the
following characteristics:
– Pooling of losses
– Fortuitous losses
– Risk transfer
– indemnification
• Pooling involves spreading losses incurred by the few over
the entire group
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Basic Characteristics of Insurance (2 of 4)
• Example of Pooling:
– Two business owners own identical buildings valued at
$50,000
– There is a 10 percent chance each building will be destroyed
by a peril in any year
– Loss to either building is an independent event
– Expected value and standard deviation of the loss for each
owner is:
Expected loss =0.90 $0 + 0.10 $ 50,000 = $ 5,000
Standard deviation = 0.90(0 − $5,000)2 + 0.10($50,000 − $5,000)2 = 15,000
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Basic Characteristics of Insurance (3 of 4)
• Example, continued:
– If the owners instead pool (combine) their loss
exposures, and each agrees to pay an equal share of
any loss that might occur:
Expected loss =0.81 $ 0 +0.09 $ 25,000+0.09 $ 25,000+ 0.01 $ 50,000
= $ 5,000
Standard deviation= 0.81(0 − $5,000)2 + 2 ∗ 0.09 ∗ ($25,000 − $5,000)2 + +0.01($50,000 − $5,000)2
= 10,607
– As additional individuals are added to the pool, the
standard deviation continues to decline while the
expected value of the loss remains unchanged
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Basic Characteristics of Insurance (3 of 4)
– As additional individuals are added to the pool, the
standard deviation continues to decline while the
expected value of the loss remains unchanged
standard deviation
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10000
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
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Law of Large Numbers
• Risk reduction is based on the Law of Large Numbers
• According to the Law of Large Numbers, the greater the
number of exposures, the more closely will the actual
results approach the probable results that are expected
from an infinite number of exposures.
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Examples of Law of Large Numbers
圖 7.1 - 每 月 道 路 交 通 意 外 趨 勢
Chart 7.1 - Trend of Monthly Road Traffic Accidents
2025/01
1 800
1 600
1 400
Number of Monthly Road Traffic Accidents
1 200
每月道路交通意外宗數
意外宗數
1 000
No. of Accidents
趨勢
800 T rend
600
400
200
0
1月 1月 1月 1月 1月 1月 1月
Jan Jan Jan Jan Jan Jan Jan
2019 2020 2021 2022 2023 2024 2025
趨勢 : 以「 X-12自迴歸 -求和 -移動平均」方法估算
Trend : Estimated by X-12 ARIMA Method
HK population: 7.5 million
Number of full driving license holders: 2.43 million (1600/2.43million =0.066%)
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Examples of Law of Large Numbers
圖 7.2 - 每 月 致 命 道 路 交 通 意 外 趨 勢
Chart 7.2 - Trend of Monthly Road Traffic Fatal Accidents
2025/01
25
20
Number of Monthly Road Traffic Fatal Accidents
每月致命道路交通意外宗數
15 致命意外宗數
No. of Fatal Accidents
趨勢
T rend
10
0
1月 1月 1月 1月 1月 1月 1月
Jan Jan Jan Jan Jan Jan Jan
2019 2020 2021 2022 2023 2024 2025
趨勢 : 以「 X-12自迴歸 -求和 -移動平均」方法估算
Trend : Estimated by X-12 ARIMA Method
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Basic Characteristics of Insurance (4 of 4)
• Fortuitous losses
– A fortuitous loss is one that is unforeseen,
unexpected, and occur as a result of chance
• Risk transfer
– A pure risk is transferred from the insured to the
insurer, who typically is in a stronger financial position
• Indemnification
– The insured is restored to his or her approximate
financial position prior to the occurrence of the loss
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Characteristics of an Ideally Insurable
Risk (1 of 3)
• Large number of exposure units
– to predict average loss based on the law of large numbers
– Negative examples: art insurance
• Accidental and unintentional loss
– to assure random occurrence of events
• Determinable and measurable loss
– to determine how much should be paid
– Difference between property and life insurance:
market value VS decided by the insured
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Characteristics of an Ideally Insurable
Risk (2 of 3)
• No catastrophic loss
– to allow the pooling technique to work
– exposures to catastrophic loss can be managed by
using reinsurance, dispersing coverage over a large
geographic area, or using financial instruments, such
as catastrophe bonds
• Calculable chance of loss
– to establish a premium that is sufficient to pay all
claims and expenses and yields a profit during the
policy period
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Characteristics of an Ideally Insurable
Risk (3 of 3)
• Economically feasible premium
– so people can afford to purchase the policy
– For insurance to be an attractive purchase, the
premiums paid must be substantially less than the face
value, or amount, of the policy
• Based on these requirements:
– Most personal, property and liability risks can be
insured
– Market risks, financial risks, production risks and
political risks are difficult to insure
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Exhibit 2.1 Fire as an Insurable Risk
Does the risk of fire satisfy the
Requirements
requirements?
1. Large number of exposure units Yes. Numerous exposure units are present.
Yes. With the exception of arson, most fire
2. Accidental and unintentional loss
losses are accidental and unintentional.
Yes. If there is disagreement over the amount
3. Determinable and measurable loss paid, a property insurance policy has provisions
for resolving disputes.
Yes. Although catastrophic fires have occurred,
4. No catastrophic loss all exposure units normally do not burn at the
same time.
Yes. Chance of fire can be calculated, and the
5. Calculable chance of loss average severity of a fire loss can be estimated
in advance.
Yes. Premium rate per $100 of fire insurance is
6. Economically feasible premium
relatively low.
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Exhibit 2.2 Unemployment as an
Insurable Risk
Requirements Does the risk of unemployment satisfy the requirements?
1. Large number of exposure units Not completely. Although there are a large number of employees, predicting
unemployment is often difficult because of the different types of unemployment
and different types of labor.
2. Accidental and unintentional Not always. Some unemployment is due to individuals who voluntarily quit their
loss jobs.
3. Determinable and measurable Not completely. The level of unemployment can be determined, but the
loss measurement of loss may be difficult. Most unemployment is involuntary
because of layoffs or because workers have completed temporary jobs.
However, some unemployment is voluntary; workers voluntarily change jobs
because of higher wages, a change in careers, family obligations, relocation to
another state, or other reasons.
4. No catastrophic loss No. A severe national recession or depressed local business conditions in a
town or city could result in a catastrophic loss.
5. Calculable chance of loss Not completely. The different types of unemployment in specific occupations
can make it difficult for actuaries to estimate the chance of loss accurately.
6. Economically feasible premium Not completely. Adverse selection, moral hazard, policy design, and the
potential for a catastrophic loss could make the insurance too expensive to
purchase. Some plans, however, will pay unemployment benefits in certain
cases where the unemployment is involuntary, and the loss payments are
relatively small, such as waiver of life insurance premiums for six months, or
payment of credit card minimum payments for a limited period.
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Adverse Selection and Insurance
• Adverse selection is the tendency of persons with a
higher-than-average chance of loss to seek insurance at
standard rates
• If not controlled by underwriting, adverse selection results
in higher-than-expected loss levels
• Adverse selection can be controlled by:
– careful underwriting (selection and classification of
applicants for insurance)
– policy provisions (e.g., suicide clause in life insurance)
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Insurance and Gambling Compared
Insurance Gambling
• Handles an already existing • Creates a new speculative
pure risk risk
• Is always socially • Is not socially productive
productive: – The winner’s gain
– both parties have a comes at the expense
common interest in the of the loser
prevention of a loss
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Insurance and Hedging Compared
Insurance Hedging
• Risk is transferred by a • Risk is transferred by a
contract contract
• Involves the transfer of • Involves risks that are
pure (insurable) risks typically uninsurable
• Moral hazard and adverse • Fewer problems of moral
selection are more severe hazard and adverse
problems for insurers selection for entities who
buy or sell futures
contracts
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Types of Insurance (1 of 5)
• Insurance can be classified as either private or
government insurance
– Private insurance includes life and health insurance as
well as property and liability insurance
– Government insurance includes social insurance
programs and other government insurance plans
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Types of Insurance (2 of 5)
• Life and Health
– Life insurance pays death benefits to beneficiaries
when the insured dies
– Health insurance covers medical expenses because
of sickness or injury
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Types of Insurance (3 of 5)
• Property and Liability
– Property insurance indemnifies property owners
against the loss or damage of real or personal
property
– Liability insurance covers the insured’s legal liability
arising out of property damage or bodily injury to others
– Casualty insurance: A broad category that covers
losses from accidents, injuries, or damage, often
including liability insurance. Think of it as a “big umbrella”
that sometimes includes both property and liability
insurance, but mainly focuses on non-property risks.
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Types of Insurance (4 of 5)
• Private insurance coverages can be grouped into two
major categories
– Personal lines: coverages that insure the real estate
and personal property of individuals and families or
provide protection against legal liability
– Commercial lines: coverages for business firms,
nonprofit organizations, and government agencies
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Types of Insurance (5 of 5)
• Social Insurance Programs
– Financed entirely or in large part by contributions from
employers and/or employees
– Benefits are heavily weighted in favor of low-income groups
– Eligibility and benefits are prescribed by statute
– Examples: Social Security, Unemployment, Workers Comp
• Other Government Insurance Programs
– Found at both the federal and state level
– Examples: Federal flood insurance, state health insurance
pools
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Benefits of Insurance to Society
• Indemnification for Loss
• Reduction of Worry and Fear
• Source of Investment Funds
• Loss Prevention
• Enhancement of Credit
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Costs of Insurance to Society (1 of 2)
• The major social costs of insurance include:
– Cost of Doing Business
▪ An expense loading is the amount needed to pay
all expenses, including commissions, general
administrative expenses, state premium taxes,
acquisition expenses, and an allowance for
contingencies and profit
– Fraudulent Claims
– Inflated Claims
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Costs of Insurance to Society (2 of 2)
• Higher premiums to cover additional losses reduce
disposable income and consumption of other goods and
services
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Learning Objectives (1 of 3)
2.1 a. Define insurance based on the definition drafted by
the Commission on Insurance Terminology.
b. Explain the basic characteristics of insurance based
on the aforementioned definition.
2.2 Explain the law of large numbers.
2.3 a. Describe the characteristics of an ideally insurable
risk from the viewpoint of a private insurer.
b. Explain whether fire and unemployment meet the
requirements of an insurable risk.
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Learning Objectives (2 of 3)
2.4 a. Understand how adverse selection can lead to
higher-than-expected losses and unprofitable business for
insurers.
b. Explain the methods insurers use to control adverse
selection.
2.5 a. Show how insurance is not the same thing as
gambling.
b. Understand how insurance differs from hedging as a
technique for treating risk.
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Learning Objectives (3 of 3)
2.6 a. Identify the major types of private insurance
companies operating in the United States today.
b. Identify important social insurance programs in the
United States.
c. Identify other government insurance programs in the
United States at the federal and state levels.
2.7 a. Explain the social and economic benefits of
insurance to society.
b. Explain the costs of insurance to society.
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