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Difficulty: MediumLaw of Large Numbers

A specialty insurance provider currently issues commercial auto and liability policies for 300 food truck operators in a single state. To improve the mathematical reliability of their premium calculations, the company executives launch a nationwide expansion to insure an additional 15,000 similar food trucks over the next two years.

According to the Law of Large Numbers, what is the primary statistical benefit the insurer achieves by increasing the number of homogeneous exposure units in this manner?

  1. The aggregate expected losses for the entire portfolio of food trucks will become more predictable, allowing the insurer to set more accurate premium rates.Answer
  2. B
    The expansion will allow the insurer to profitably cover speculative risks in addition to pure risks, since the massive pool guarantees a financial gain.
  3. C
    By adding a massive volume of policies, the insurer is practicing risk avoidance, which entirely eliminates the possibility of catastrophic claims.
  4. D
    The insurer will automatically shift direct legal liability for the new food truck claims to an assuming reinsurer, completely bypassing the need for primary underwriting.

Answer

The aggregate expected losses for the entire portfolio of food trucks will become more predictable, allowing the insurer to set more accurate premium rates.
The Law of Large Numbers states that as the number of homogeneous exposure units (in this case, similar food truck operations) increases, the statistical accuracy of predicting aggregate future losses improves. This increased predictability allows the insurance company's actuaries to set more accurate, mathematically sound premium rates for the entire portfolio.

Step-by-Step Solution

1
Analyze the scenario to identify the core principle being tested.
The scenario involves increasing the number of insured risks (food trucks) from 300 to over 15,000 to improve mathematical reliability.
Identifying the underlying insurance mechanism is necessary to determine the outcome of expanding a pool of similar risks.
2
Define the Law of Large Numbers.
It is a statistical principle stating that as the number of similar (homogeneous) exposure units increases, the actual losses will more closely match the mathematically expected losses.
This definition links the increased portfolio size to the specific statistical benefits gained by the insurer.
3
Evaluate the options against the correct application of this principle.
The insurer gains greater predictability for the aggregate losses of the group, which stabilizes ratemaking and premium pricing. It does not alter the nature of the risk, avoid risk entirely, or shift liability to reinsurers.
Applying the exact definition ensures the selected answer reflects the true actuarial purpose of the Law of Large Numbers.

Key Concept

The Law of Large Numbers and its impact on the predictability of aggregate losses for homogeneous exposure units.
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Topics

Law of Large Numbers

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