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Difficulty: MediumLaw of Large Numbers

A workers' compensation insurance carrier is incorporating several thousand similar artisan contractor businesses (such as midwestern plumbers and electricians) into its existing book of business. The carrier's chief actuary is analyzing how this massive influx of homogeneous exposure units will impact the company's ratemaking and reserving practices over the next decade. Based on the principles of the Law of Large Numbers, which of the following statements describe the correct actuarial outcomes of this expansion? (Select two)

  1. The statistical variance between the carrier's expected overall claims and the actual claims experienced by this group will decrease.Answer
  2. The carrier's ability to accurately forecast the aggregate financial impact of future claims for this expanded portfolio will significantly improve.Answer
  3. C
    The massive volume of new policies transforms these exposures from pure risks into speculative risks, guaranteeing an underwriting profit.
  4. D
    The carrier is effectively utilizing risk avoidance, as the sheer size of the portfolio mathematically prevents any individual severe injury from occurring.
  5. E
    The primary carrier assumes direct liability for all catastrophic events without the need for reinsurance, since the large volume of policies automatically neutralizes severity.

Answer

The correct statements are that the statistical variance between expected and actual claims will decrease, and the carrier's ability to forecast aggregate future claims will significantly improve.
The Law of Large Numbers dictates that as a pool of homogeneous (similar) exposure units grows, the insurer can more accurately predict the aggregate losses that the pool will experience. This mathematical certainty leads to a tighter statistical variance between what the actuaries expect to happen and what actually happens.

Step-by-Step Solution

1
Analyze the core definition of the Law of Large Numbers in an insurance context.
The Law states that as the number of homogeneous exposure units increases, the predictability of future aggregate losses improves.
This principle is the mathematical foundation for setting accurate insurance rates.
2
Evaluate the correct options against this definition.
Decreased statistical variance and improved forecasting of aggregate claims perfectly describe the outcomes of adding thousands of similar exposures.
Larger numbers smooth out the extremes, bringing actual results closer to expected probabilities.
3
Rule out the incorrect options based on limitations of the Law.
The Law does not change pure risk to speculative risk, does not constitute risk avoidance, and does not eliminate the need for reinsurance against catastrophic severity.
Understanding what the Law of Large Numbers cannot do is just as important as knowing what it can do.

Key Concept

The Law of Large Numbers improves the predictability of aggregate losses for homogeneous groups, but it cannot predict individual losses or prevent catastrophic severity.
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Topics

Law of Large Numbers

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