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Difficulty: HardLaw of Large Numbers

A commercial auto insurer currently writes liability policies for 500 identical delivery vans in a single metropolitan area. To stabilize premium pricing, the chief actuary recommends expanding operations nationwide to insure 100,000 similar vans. According to the Law of Large Numbers, which of the following best describes the actuarial outcome of this expansion?

  1. The variance between the insurer's projected aggregate losses and actual experienced losses will decrease, though it remains impossible to predict which specific vans will suffer a loss.Answer
  2. B
    The insurer's overall portfolio transforms from a pure risk to a speculative risk because the massive volume of premiums collected introduces the possibility of a guaranteed underwriting gain.
  3. C
    The insurer has effectively utilized risk avoidance, as absorbing a significantly larger volume of delivery vans eliminates the underlying physical hazards that cause accidents.
  4. D
    The massive increase in exposure units automatically transfers the primary contractual liability to a reinsurer, relieving the original insurer of direct responsibility for individual claims.

Answer

The variance between the insurer's projected aggregate losses and actual experienced losses will decrease, though it remains impossible to predict which specific vans will suffer a loss.
The correct answer correctly isolates the dual nature of the Law of Large Numbers: it grants insurers the ability to highly accurately forecast the total volume and monetary value of claims across a massive pool of homogeneous units, while explicitly maintaining that individual claim events remain random and completely unpredictable.

Step-by-Step Solution

1
Analyze the core principle of the Law of Large Numbers.
The law states that a larger number of similar exposure units allows for more accurate prediction of future aggregate losses.
This is the foundational statistical concept behind insurance pricing and risk pooling.
2
Apply the principle to the provided scenario of increasing vans from 500 to 100,000.
The insurer will be able to predict the total amount of losses for the 100,000 vans much more accurately than for the 500 vans.
The larger sample size reduces statistical variance in the aggregate outcome.
3
Identify the limitation of the Law of Large Numbers.
The law applies only to the aggregate group, not to individual units.
Even with 100,000 vans, the insurer cannot predict exactly which van will be involved in an accident tomorrow.

Key Concept

The Law of Large Numbers improves aggregate loss predictability but does not predict individual losses.
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Topics

Law of Large Numbers

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