Ch1. Introduction to Insurance — Risk Management and the Nature of Insurance

Risk and Risk Management

Risk Defined:
The possibility of a loss occurring
Uncertainty about outcomes

Types of Risk:
Pure risk: only a loss can occur (insurable)
Speculative risk: gain or loss both possible (not insurable)

The Four Risk Management Methods:
Avoidance: stop the activity that creates risk
Reduction: lower the frequency or severity of loss
Retention: absorb the loss yourself (self-insurance)
Transfer: shift the risk to another party → insurance

Insurance = a risk transfer mechanism

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The Definition and Principles of Insurance

Insurance Defined:
A large group of individuals facing similar risks
each pay premiums into a common pool;
when a covered loss occurs, the pool pays out.

Law of Large Numbers:
As the number of observations increases,
actual loss rates converge to expected loss rates.
This is the actuarial foundation for premium setting.

Equivalence Principle (Premium-Loss Balance):
Total premiums collected = Total claims paid
(measured on a net/pure premium basis)

Contribution Principle (Individual Equity):
Each insured's premium is proportional to their risk level.

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Requirements for an Insurable Risk

An Insurable Risk Must Be:
Large number of similar exposure units
Accidental (no intentional losses)
Definite and measurable loss
Not catastrophic (not a systemic wipe-out)

Elements of an Insurance Contract:
Insurer: the insurance company (pays claims)
Policyholder: pays premiums
Insured: the person or property covered
Beneficiary: receives the claim payment

Premium Components:
Net/pure premium: funds claim payments
Loading: covers operating expenses and profit

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Key Concept Cards

4 Risk Management Methods = Avoid, Reduce, Retain, Transfer ★★★★★ : Avoidance, Reduction, Retention, Transfer. Memory hook: A-R-R-T

Insurance is Built on the Law of Large Numbers ★★★★★ : Pooling many exposures makes loss prediction reliable. Memory hook: Insurance = pooling + LLN

Premium-Loss Balance = Premiums In = Claims Out ★★★★☆ : On a net premium basis, inflows equal outflows. Memory hook: Balance = in equals out

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Practice Quiz

Q. Why is speculative risk not insurable?

Insurance covers only pure risk — situations where only a loss can occur. Speculative risk allows for either gain or loss (e.g., stock investments). Insuring speculative risk creates moral hazard: the insured might intentionally trigger a “loss” to capture a gain. It also invites adverse selection: only those expecting losses would buy the policy. Additionally, the Law of Large Numbers is hard to apply because outcomes are not homogeneous. Examples: stock market losses, business failure — these cannot be insured.

Q. How does the Law of Large Numbers apply to premium pricing?

The Law of Large Numbers states that as the number of observations grows, actual outcomes approach theoretical probabilities. A small pool of policies means high prediction error → unstable premiums. A large pool allows accurate loss forecasting → stable premiums. Life insurers rely on large mortality databases to price products; property insurers use large fire-loss databases. The core insight: the larger the insurance pool, the more accurate and stable the premium.