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Difficulty: MediumLaw of Large Numbers

A commercial underwriter is reviewing a book of business consisting of several thousand independent veterinary clinics. To achieve greater rate stability and ensure premium solvency, the underwriter recommends expanding the pool to include tens of thousands of similar clinics nationwide. According to the foundational principles of insurance pricing, what is the primary statistical benefit of this expansion strategy?

  1. The accuracy of predicting total aggregate losses for the group will improve, even though the insurer still cannot forecast which specific clinics will suffer a loss.Answer
  2. B
    The larger volume of clinics allows the insurer to generate sufficient premium to cover both the pure risks of property damage and the speculative risks of business investments.
  3. C
    The expansion serves as a method of risk avoidance, completely eliminating the financial uncertainty associated with insuring small commercial operations.
  4. D
    The increased pool size automatically transfers the direct legal liability for any individual clinic's catastrophic claims to an assuming reinsurer.

Answer

The accuracy of predicting total aggregate losses for the group will improve, even though the insurer still cannot forecast which specific clinics will suffer a loss.
The correct answer accurately defines the operational outcome of the Law of Large Numbers. By increasing the number of similar exposure units (the veterinary clinics), the insurer drastically reduces the statistical variance in its loss projections. This mathematical certainty allows the insurer to set stable, solvent premium rates based on highly predictable aggregate losses, even though it remains impossible to know precisely which individual clinic will file a claim.

Step-by-Step Solution

1
Analyze the underwriter's proposed strategy.
The underwriter is significantly increasing the number of similar (homogeneous) exposure units within a specific risk pool.
Identifying the action is necessary to determine which insurance principle is being applied.
2
Connect the strategy to the corresponding actuarial principle.
Increasing homogeneous exposure units invokes the Law of Large Numbers.
The Law of Large Numbers is the mathematical foundation that allows insurers to predict future losses accurately.
3
Determine the precise statistical outcome and limitation of this principle.
As the pool size grows, the variance between expected and actual aggregate losses decreases, stabilizing rates. However, it provides no predictive power regarding which individual unit will actually experience a loss.
Understanding both the benefit (aggregate predictability) and limitation (no individual predictability) is required to select the correct conclusion.

Key Concept

Law of Large Numbers
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Topics

Law of Large Numbers

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