Match each underwriting scenario or action regarding the Law of Large Numbers with its corresponding statistical or actuarial outcome.
- Increasing the total volume of identical exposure units within a specific insurance portfolioReduces the relative deviation between actual aggregate losses and expected aggregate losses.
- Attempting to forecast the precise loss outcome for one specific policyholderRemains impossible because statistical predictability does not apply to single exposure units.
- Merging dissimilar risk profiles, such as hazardous manufacturing and retail clothing, into a single risk poolViolates the requirement for homogeneity, making aggregate predictions unreliable.
- Relying on decades of mortality data from millions of individuals to price a new life insurance productDemonstrates the practical application of sufficient data volume to achieve actuarial certainty.
Answer
1 matches with reducing relative deviation, 2 matches with remaining impossible for single units, 3 matches with violating homogeneity, and 4 matches with achieving actuarial certainty.
Each matching pair accurately reflects a core principle of the Law of Large Numbers. A larger pool of similar risks reduces aggregate variance, but requires homogeneity to be valid. Furthermore, while it provides actuarial certainty for the whole pool, it fundamentally cannot predict specific, individual losses.
Step-by-Step Solution
Key Concept
The Law of Large Numbers states that as the number of independent, homogeneous exposure units increases, the actual aggregate losses will more closely approximate the expected aggregate losses, though it cannot predict individual losses.