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Difficulty: MediumLaw of Large Numbers

A life insurance provider recently issued policies to a national trade association comprising 25,000 members with similar occupational profiles. Based on the law of large numbers, what is the primary statistical benefit the insurer gains from covering this specific population?

  1. It allows the insurer to reliably predict the aggregate volume of claims that will occur within the group over the policy period.Answer
  2. B
    It enables the underwriter to pinpoint which individual members are most likely to file a mortality claim.
  3. C
    It guarantees that the insurer will avoid speculative risks when setting the premium rates for the association.
  4. D
    It automatically cedes a portion of the aggregate liability to an assuming insurer to prevent insolvency.

Answer

It allows the insurer to reliably predict the aggregate volume of claims that will occur within the group over the policy period.
The law of large numbers states that as the number of similar (homogeneous) exposure units increases, the accuracy of predicting future aggregate losses improves. This mathematical principle allows the insurer to forecast the total volume of claims for the entire association reliably, which is necessary for establishing sound premium rates.

Step-by-Step Solution

1
Identify the core principle of the law of large numbers.
The principle states that as the number of similar exposure units increases, the actual losses will more closely approach the mathematically expected losses.
This is the foundational concept that allows insurance companies to set accurate premiums.
2
Apply the principle to the provided scenario.
The scenario involves 25,000 members (a sufficiently large pool) who share similar profiles (homogeneous exposure units), which allows the insurer to forecast the total losses for the entire group accurately.
The law of large numbers creates predictability in the aggregate, even though individual outcomes remain entirely unpredictable.

Key Concept

The law of large numbers increases the accuracy of aggregate loss predictions when applied to a large pool of homogeneous exposure units.
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Topics

Law of Large Numbers

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