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Difficulty: MediumLaw of Large Numbers

An insurance company relies on the Law of Large Numbers to establish statistically sound premium rates for its property and casualty policies. Which of the following statements correctly describe the application and outcomes of this principle? (Select two)

  1. As the number of homogeneous exposure units increases, the actual losses experienced will more closely approximate the expected losses.Answer
  2. The principle improves the insurer's ability to predict aggregate losses for the entire pool, rather than forecasting individual losses.Answer
  3. C
    Expanding the number of exposure units allows the insurer to convert uninsurable speculative risks into insurable pure risks.
  4. D
    By relying on this statistical principle to pool exposures, the insurer is employing the risk management technique of risk avoidance.

Answer

The correct statements are that actual losses will more closely approximate expected losses as the pool grows, and that the principle predicts aggregate losses rather than individual losses.
The Law of Large Numbers is a statistical theorem fundamentally relied upon by insurers. It states that as the number of similar, independent exposure units (homogeneous risks) increases, the statistical variance decreases, causing the actual losses to more closely align with predicted probabilities. This allows insurers to accurately forecast the aggregate losses for the entire portfolio and set appropriate premiums, even though it remains impossible to predict which specific insureds will actually experience a loss.

Step-by-Step Solution

1
Define the core mechanism of the Law of Large Numbers.
It states that a larger sample size yields a more accurate prediction of future events.
This establishes why actual losses approach expected losses as the pool of homogeneous risks increases.
2
Differentiate between aggregate and individual predictability.
The principle applies to the entire group, meaning total losses become predictable, but predicting exactly who will suffer a loss remains impossible.
This confirms the second correct statement regarding aggregate versus individual forecasting.
3
Evaluate the incorrect statements against foundational risk concepts.
Speculative risks cannot be insured regardless of pool size, and buying insurance constitutes risk transfer, not risk avoidance.
This eliminates the distractors.

Key Concept

The Law of Large Numbers ensures that as a pool of independent, homogeneous risks grows, aggregate losses become statistically predictable, enabling accurate premium calculations.
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Topics

Law of Large Numbers

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