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Difficulty: MediumLaw of Large Numbers

A regional property insurance company recently increased its pool of insured residential homes from 2,000 to 50,000 similar properties with comparable valuations. According to the law of large numbers, how does this significant expansion primarily benefit the insurer's underwriting process?

  1. A
    It converts the uninsurable speculative risks of the new properties into insurable pure risks.
  2. B
    It allows the insurer to precisely predict which specific homes will experience a loss during the policy period.
  3. C
    It automatically shifts the primary liability of the expanded property pool to an assuming reinsurer.
  4. It improves the statistical accuracy of predicting the aggregate future losses for the entire group.Answer

Answer

It improves the statistical accuracy of predicting the aggregate future losses for the entire group.
The correct answer accurately reflects the statistical foundation of insurance. As an insurer acquires a larger number of similar, independent exposure units, the law of large numbers dictates that actual overall losses will more closely approach expected losses, which allows underwriters to set premiums more accurately.

Step-by-Step Solution

1
Define the core principle of the law of large numbers in an insurance context.
The law of large numbers states that a larger number of similar exposure units leads to more predictable and accurate aggregate loss estimates.
Understanding the definition is required to determine the benefit to the insurer.
2
Evaluate the outcome of increasing the pool from 2,000 to 50,000 properties.
With a significantly larger pool of homogeneous properties, the insurer's expected losses will closely mirror the actual losses experienced by the group as a whole.
This directly connects the statistical theory to the practical underwriting benefit of rate stability.
3
Distinguish between aggregate prediction and individual prediction.
The principle only applies to the group's overall total loss, not to predicting the fate of any single specific property.
This distinction is critical to eliminate common misunderstandings about risk pooling.

Key Concept

Law of Large Numbers
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Topics

Law of Large Numbers

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