Chapter 2 Notes: Insurance and Risk

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 pecuniary benefits on their occurrence, or to render services connected with the risk.

Basic Characteristics of Insurance

• (1 of 4) Pooling of losses

  • Losses incurred by the few are spread over the entire group.

  • Risk reduction is based on the Law of Large Numbers: the greater the number of exposures, the more closely the actual results will approach the probable results as if from an infinite number of exposures.

• (2 of 4) Example of Pooling

  • Two business owners own identical buildings valued at $50{,}000$.

  • Each building has a 10 ext{%} chance of being destroyed by a peril in any year.

  • Loss to either building is an independent event.

  • For each owner, the expected value (EV) and standard deviation (SD) of the loss are:

  • EV for each owner: $EV = p imes L = 0.10 imes 50{,}000 = 5{,}000$

  • Variance for each owner: $\text{Var} = p(1-p)L^2 = 0.10 \times 0.90 \times (50{,}000)^2$

  • SD for each owner: $\text{SD} = L\sqrt{p(1-p)} = 50{,}000 \sqrt{0.10 \times 0.90} = 50{,}000 \times 0.3 = 15{,}000$

• (3 of 4) Example, continued

  • If the two owners pool (combine) their loss exposures and each pays an equal share of any loss that might occur:

  • As additional individuals are added to the pool, the standard deviation declines while the expected value of the loss remains unchanged.

• (4 of 4) Payment of fortuitous losses; Risk transfer; Indemnification

  • Fortuitous loss: unforeseen, unexpected, and due to chance.

  • Risk transfer: a pure risk is transferred from the insured to the insurer, which is typically in a stronger financial position.

  • Indemnification: the insured is restored to approximately the financial position prior to the loss.

Characteristics of an Ideally Insurable Risk

• (1 of 3) Large number of exposure units

  • Enables prediction of average loss via the law of large numbers.

• (2 of 3) Accidental and unintentional loss

  • Ensures random occurrence of events.

• (3 of 3) Determinable and measurable loss

  • Allows determination of how much should be paid.

• (4 of 3) No catastrophic loss

  • Catastrophic losses undermine pooling; managed via reinsurance, geographic dispersion, or catastrophe bonds.

• (5 of 3) Calculable chance of loss

  • Establishes a premium sufficient to pay claims and expenses and yield profit during the policy period.

• (6 of 3) Economically feasible premium

  • Premiums must be substantially less than the face value of the policy to be attractive.

• Conclusion: Based on these requirements, most personal, property, and liability risks can be insured; market, financial, production, and political risks are harder to insure.

Exhibits: Insurability of Specific Risks

• Exhibit 2.1 Fire as an Insurable Risk

  1. Large number of exposure units: Yes (numerous exposure units).

  2. Accidental and unintentional loss: Yes (except arson, most fires are accidental/unintentional).

  3. Determinable and measurable loss: Yes (disputes resolved by policy provisions).

  4. No catastrophic loss: Yes (in general not all burn at once).

  5. Calculable chance of loss: Yes (chance and average severity can be estimated).

  6. Economically feasible premium: Yes (premium rate per $$100 of fire insurance is relatively low).

• Exhibit 2.2 Unemployment as an Insurable Risk

  1. Large number of exposure units: Not completely (large number of employees, but unemployment types vary—difficult to predict).

  2. Accidental and unintentional loss: Not always (some unemployment occurs when individuals voluntarily quit).

  3. Determinable and measurable loss: Not completely (loss measurement possible, but difficult).

  4. No catastrophic loss: No (severe national recession or local economic downturn could cause a catastrophe).

  5. Calculable chance of loss: Not completely (different unemployment types across occupations complicate estimates).

  6. Economically feasible premium: Not completely (adverse selection, moral hazard, policy design, and potential for catastrophic loss can make premiums high; some plans exist for involuntary unemployment with limited benefits such as premium waivers or limited continuation payments).

Adverse Selection and Insurance

• Adverse selection: tendency of individuals with a higher-than-average chance of loss to seek insurance at standard rates.

• If not controlled by underwriting, adverse selection leads to higher-than-expected losses.

• Controls include:

  • Underwriting: careful selection and classification of applicants for insurance.

  • Policy provisions: e.g., suicide clause in life insurance.

Insurance vs. Gambling

• Insurance

  • Handles an existing pure risk.

  • Is always socially productive: both parties have a common interest in loss prevention.

• Gambling

  • Creates a new speculative risk.

  • Not socially productive: winner’s gain comes at the expense of the loser.

Insurance vs. Hedging

• Insurance

  • Risk transferred by a contract.

  • Involves transfer of pure (insurable) risks.

  • Moral hazard and adverse selection are more severe problems for insurers.

• Hedging

  • Risk transferred by a contract.

  • Involves risks that are typically uninsurable.

  • Fewer problems of moral hazard and adverse selection for entities using futures contracts.

Types of Private Insurance (1 of 3)

• Life and Health

  • Life insurance pays death benefits to beneficiaries when the insured dies.

  • Health insurance covers medical expenses due to sickness or injury.

Types of Private Insurance (2 of 3)

• Property and Liability

  • Property insurance indemnifies property owners against loss or damage of real or personal property.

  • Liability insurance covers the insured’s legal liability arising from property damage or bodily injury to others.

  • Casualty insurance refers to coverage not covered by fire, marine, or life insurance.

Types of Private Insurance (3 of 3)

• Private insurance coverages are grouped into two major categories:

  • Personal lines: cover real estate and personal property of individuals/families or provide protection against legal liability.

  • Commercial lines: coverages for business firms, nonprofit organizations, and government agencies.

Types of Government Insurance

• Social Insurance Programs

  • Financed largely by contributions from employers and/or employees.

  • Benefits are heavily weighted toward low-income groups.

  • Eligibility and benefits are prescribed by statute.

  • Examples: Social Security, Unemployment, Workers’ Compensation.

• Other Government Insurance Programs

  • Found at federal and state levels.

  • Examples: Federal flood insurance, state health insurance pools.

Social Benefits of Insurance

• Indemnification for loss.

• Reduction of worry and fear.

• Source of investment funds.

• Loss prevention.

• Enhancement of credit.

Social Costs of Insurance

• Cost of doing business

  • An expense loading covers commissions, general admin expenses, premium taxes, acquisition expenses, contingencies, and profit.

• Fraudulent claims.

• Inflated claims

  • Higher premiums to cover additional losses reduce disposable income and consumption of other goods and services.

Note: All content mirrors the key ideas and wording from the provided transcript. Numerical examples include explicit calculations for the pooling example where appropriate, using standard actuarial formulas.