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Difficulty: EasyLaw of Large Numbers

A syndicate currently provides liability coverage to 600 independent artisan contractors. To stabilize its rate-setting process, the syndicate plans to broaden its market reach to include 85,000 contractors with identical risk profiles. Under the Law of Large Numbers, what is the direct mathematical result of this membership growth?

  1. The projections of aggregate future claims become far more reliable and closely match actual outcomes.Answer
  2. B
    The contractors' uninsurable speculative risks are mathematically converted into insurable pure risks.
  3. C
    The syndicate's direct liability for claim payments is transferred to an assuming reinsurer.
  4. D
    The overall risk handling method successfully shifts from risk retention to risk avoidance.

Answer

The projections of aggregate future claims become far more reliable and closely match actual outcomes.
The correct answer accurately reflects the core definition of the Law of Large Numbers. In insurance, as the number of independent, identically distributed exposure units (in this case, artisan contractors) increases, the actual overall losses will more closely approach the expected losses, making rate-setting highly reliable.

Step-by-Step Solution

1
Identify the core insurance concept being tested.
The question asks about the primary benefit of the Law of Large Numbers when expanding an insurance pool.
Understanding the definition of the concept is necessary to evaluate the given scenario.
2
Analyze the specific scenario provided.
The insurer is increasing its pool of homogeneous exposure units from 600 to 85,000.
This confirms the foundational requirement for the Law of Large Numbers to operate effectively.
3
Determine the outcome of applying the concept to the scenario.
A significantly larger pool of similar risks reduces statistical variance, allowing the insurer to predict total group losses with much greater accuracy.
This predictability is the fundamental reason insurers can safely calculate and charge stable premiums.

Key Concept

Law of Large Numbers
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Topics

Law of Large Numbers

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