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Difficulty: HardLaw of Large Numbers

A regional property insurer is analyzing its current portfolio of 100 coastal commercial buildings. The chief actuary recommends expanding this specific portfolio to 10,000 similar buildings across multiple states to optimize their pricing models. Based on the Law of Large Numbers, how will this expansion most accurately impact the insurer's actuarial calculations and risk profile?

  1. The total losses for the entire portfolio will align more closely with expected actuarial projections, but the insurer will remain unable to predict which specific buildings will suffer a loss.Answer
  2. B
    The increased predictability allows the insurer to engage in risk avoidance by identifying exactly which individual buildings will experience claims and declining to renew those specific policies.
  3. C
    Expanding the number of covered properties transforms the pure risk of property damage into a speculative risk, legally guaranteeing an underwriting profit for the insurer on the expanded portfolio.
  4. D
    The expansion requires the primary insurer to cede the portfolio to a reinsurer, as the primary insurer transfers direct legal liability for claim payments to the reinsurer when utilizing large numbers.

Answer

The total losses for the entire portfolio will align more closely with expected actuarial projections, but the insurer will remain unable to predict which specific buildings will suffer a loss.
The correct answer accurately reflects that increasing the pool size of similar exposure units reduces statistical variance, making total group losses highly predictable for rate-making. Crucially, it also acknowledges the fundamental limitation of the concept: individual losses within that pool remain entirely random and cannot be predicted.

Step-by-Step Solution

1
Identify the core principle of the Law of Large Numbers.
The principle states that as the number of independent, homogeneous exposure units increases, the actual aggregate losses will more closely approach the expected aggregate losses.
This is the foundational statistical concept insurers use to set accurate premium rates for a large pool of risks.
2
Determine the limitations of this mathematical principle.
While the total volume and monetary amount of losses for the group become highly predictable, the specific identity of the individual units that will suffer those losses remains entirely random and unpredictable.
Insurance is based on pooling uncertainty; if individual losses were perfectly predictable, the concept of risk transfer would fail.
3
Apply the principle to the scenario of expanding from 100 to 10,000 buildings.
The expansion satisfies the requirement for a larger pool of exposure units, meaning the insurer can accurately predict the portfolio's total losses, but cannot single out which of the 10,000 buildings will be damaged.
This confirms the correct application of the concept without falling for common traps regarding individual prediction.

Key Concept

The Law of Large Numbers allows insurers to accurately predict aggregate group losses by pooling many similar exposure units, but it does not allow for the prediction of individual losses.
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Topics

Law of Large Numbers

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