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Zorluk: KolayLaw of Large Numbers

An insurance company is increasing the number of similar personal auto policies it writes in a specific region. According to the Law of Large Numbers, which of the following outcomes will the insurer experience as the size of this risk pool grows? (Select two)

  1. The accuracy of the insurer's total predicted losses for the group will improve.Cevap
  2. B
    The insurer will be able to identify precisely which individual policies will experience a loss.
  3. The actual total losses experienced by the group will more closely match the mathematically expected losses.Cevap
  4. D
    The insurer will be able to safely offer coverage for speculative risks.

Cevap

The outcomes where the accuracy of total predicted losses improves and actual losses more closely match expected losses.
The correct statements accurately reflect that a larger pool of homogeneous exposure units allows the insurer to better predict overall losses for the group, meaning actual losses will closely mirror expected losses. This forms the mathematical foundation of insurance ratemaking and stability.

Adım Adım Çözüm

1
Analyze the core principle of the Law of Large Numbers.
It states that a larger number of similar exposure units increases the predictability of future losses for the entire group.
Understanding the basic definition is required to determine its effects on an insurance pool.
2
Evaluate the options based on group predictability versus individual predictability.
The principle applies to aggregate (total) group prediction and statistical variance, not individual prediction or the type of risk.
This distinguishes the correct outcomes from common misconceptions about individual forecasting and speculative risks.

Anahtar Kavram

The Law of Large Numbers improves the statistical predictability of aggregate losses as the pool of homogeneous risks grows.
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Law of Large Numbers

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