Match each underwriting or portfolio scenario with its corresponding outcome based on the principles of the Law of Large Numbers.
- Expanding a regional portfolio by adding 40,000 similar residential properties.Enhances the accuracy of overall loss forecasts and stabilizes premium pricing.
- Grouping heavy industrial manufacturers together with small administrative offices for rating purposes.Compromises predictability by violating the requirement for homogeneous exposure units.
- Operating a niche insurance program with a highly limited pool of only 75 insured vehicles.Results in a high degree of variance between actual and expected losses due to insufficient sample size.
- Attempting to identify the precise policyholder who will file a catastrophic claim during the policy period.Falls outside the scope of actuarial models, as the principle only predicts aggregate group trends.
Answer
Expanding the portfolio matches with enhanced accuracy. Grouping dissimilar risks matches with violating homogeneous requirements. Operating a small pool matches with high variance. Predicting a specific individual's claim matches with falling outside actuarial scope.
Each scenario maps directly to a core operational rule of the Law of Large Numbers. Large, homogeneous pools yield accurate, stable actuarial predictions. Small pools yield volatile financial results. Dissimilar pools ruin the statistical foundation. Furthermore, the law is solely a tool for aggregate group forecasting, never for individual event prediction.
Step-by-Step Solution
Key Concept
Law of Large Numbers Mechanics (Sample Size, Homogeneity, and Predictability)