As risk pools grow, what happens to the insurer's risk due to the law of large numbers?

As risk pools grow, what happens to the insurer's risk due to the law of large numbers?

• A. It increases unbounded
• B. It fluctuates unpredictably
• C. It decreases and approaches zero
• D. It remains the same

Answer: (C)

As the pool of insured grows, the variability in losses per policy declines because independent claims tend to cancel each other out. The law of large numbers shows that the average claim per policy converges to the expected claim as the number of policies increases. This means the insurer becomes more shielded from random swings in total losses, and the risk associated with deviations from expected losses shrinks toward zero in relative terms. So, even though total losses can increase with more policies, the relative risk (the likelihood of large deviations from the expected loss ratio) approaches zero. That’s why the best choice is that the insurer’s risk decreases and approaches zero. The other options don’t fit: risk does not grow unbounded, it does not remain the same, and it doesn’t fluctuate unpredictably as pool size grows.

As the pool of insured grows, the variability in losses per policy declines because independent claims tend to cancel each other out. The law of large numbers shows that the average claim per policy converges to the expected claim as the number of policies increases. This means the insurer becomes more shielded from random swings in total losses, and the risk associated with deviations from expected losses shrinks toward zero in relative terms. So, even though total losses can increase with more policies, the relative risk (the likelihood of large deviations from the expected loss ratio) approaches zero.

That’s why the best choice is that the insurer’s risk decreases and approaches zero. The other options don’t fit: risk does not grow unbounded, it does not remain the same, and it doesn’t fluctuate unpredictably as pool size grows.