In the context of the Law of Large Numbers, insurance ratemaking depends on specific mathematical conditions. Match each portfolio characteristic or insurer decision below with its direct impact on loss predictability.
- Combining commercial trucking risks with residential jewelry coverage in a single pricing block.Violates the homogeneity requirement, rendering aggregate loss projections mathematically invalid.
- Expanding a standardized term-life insurance portfolio from 5,000 to 500,000 policyholders.Maximizes aggregate predictability and stabilizes premiums through variance reduction.
- Writing specialized property coverage for a total market of only 15 unique, experimental research facilities.Produces highly volatile loss outcomes due to an insufficient volume of exposure units.
- Attempting to calculate the exact future date of a specific policyholder's auto accident.Remains statistically impossible regardless of the overall size or credibility of the risk pool.
Answer
Combining different risks violates homogeneity; Expanding the portfolio maximizes aggregate predictability; Writing for 15 unique facilities produces volatile outcomes due to insufficient volume; Predicting a specific individual's loss remains statistically impossible.
Each scenario directly illustrates a core facet of the Law of Large Numbers. Expanding homogeneous pools reduces variance; small pools cause volatility; mixed risks break the homogeneity rule; and individual predictions remain impossible.
Step-by-Step Solution
Key Concept
The Law of Large Numbers requires a massive volume of homogeneous exposure units to predict aggregate loss, but it can never predict individual loss events.