Match each practical underwriting scenario with the specific principle or limitation of the Law of Large Numbers that it best illustrates.
- An underwriter segments a commercial fleet portfolio into distinct classes based on vehicle weight, primary radius of operation, and cargo type.Satisfies the requirement that exposure units must be homogeneous for accurate loss prediction.
- A property carrier accumulates 250,000 policies by indiscriminately mixing coastal wind-exposed properties with inland homes under a uniform pricing structure.Demonstrates that a massive sample size cannot overcome the fundamental flaw of pooling heterogeneous risks.
- An actuary projects that expanding a group health plan from 2,000 to 20,000 members will significantly narrow the margin of error in next year's loss forecast.Illustrates the core mathematical principle that greater pool size reduces relative variance in expected losses.
- A casualty insurer accurately forecasts 500 workers' compensation claims across a massive manufacturing pool, yet cannot determine which specific factories will experience them.Reflects the limitation that aggregate portfolio predictability provides no certainty regarding individual risk outcomes.
Cevap
The correct matches align homogeneous risk segmentation with predictability requirements, heterogeneous risk mixing with pooling failures, sample size increases with variance reduction, and aggregate forecasting with the inability to predict individual losses.
Each scenario correctly maps to a core facet of the Law of Large Numbers: the necessity of homogeneous units, the mathematical reduction in variance as sample size grows, the inability to predict individual losses, and the failure of sheer volume to offset heterogeneous risks.
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Anahtar Kavram
The effectiveness of the Law of Large Numbers relies on a large volume of homogeneous exposure units to predict aggregate losses accurately, while recognizing it cannot predict individual outcomes.
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