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Difficulty: MediumLaw of Large Numbers

An underwriter for a regional casualty carrier is reviewing the statistical reliability of the company's loss forecasts for a professional liability portfolio. The portfolio currently experiences highly erratic year-over-year claims totals due to limited enrollment. According to the foundational statistical principles used in insurance ratemaking, what is the most effective way for the carrier to ensure that actual aggregate losses will consistently and closely approximate anticipated losses?

  1. Expand the portfolio by accumulating a substantial volume of independent, statistically homogeneous exposure unitsAnswer
  2. B
    Introduce speculative risk coverages into the existing portfolio to mathematically offset the financial volatility of the pure liability claims
  3. C
    Instruct the existing policyholders to practice complete risk avoidance by ceasing all professional operations that generate liability exposure
  4. D
    Execute an agreement where a reinsurer assumes direct contractual liability to the individual policyholders for all future claims

Answer

Expand the portfolio by accumulating a substantial volume of independent, statistically homogeneous exposure units.
The correct answer directly applies the Law of Large Numbers. In insurance ratemaking, predictability improves only when a large volume of similar (homogeneous) and independent risks are pooled together. This mathematical principle ensures that while individual losses remain unknown, the aggregate sum of losses will closely mirror the actuary's predicted loss ratio.

Step-by-Step Solution

1
Identify the core actuarial problem presented in the scenario.
The carrier is facing erratic, unpredictable claims totals because the portfolio has limited enrollment (a small risk pool).
Accurate ratemaking requires a predictable pattern of losses, which is mathematically impossible with a small sample size.
2
Determine which foundational statistical principle resolves this specific problem.
The Law of Large Numbers provides the mechanism to stabilize expected losses.
This law states that as the number of units increases, the statistical variance decreases.
3
Select the option that correctly satisfies the conditions of this mathematical law.
The carrier must accumulate a substantial volume of independent, statistically homogeneous (similar) exposure units.
For the Law of Large Numbers to operate effectively and predict aggregate losses accurately, the expanded pool must consist of independent risks that share similar loss characteristics.

Key Concept

The Law of Large Numbers requires a massive pool of similar, independent exposure units to accurately forecast aggregate losses and stabilize premium pricing.
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Topics

Law of Large Numbers

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