Question

What is the "law of large numbers" in insurance theory?

Answer 1

The Law of Large Numbers is the principal that backstops much of statistical work. It states that as the number of experiments or trials with the same likelihood grows, the results will become increasingly orderly and follow a pattern.

 

For instance, if I take a coin and flip it once, I only have a 50% chance of guessing the outcome of the flip as tails. However, if I flip the coin 1000 times, I have a much better chance of guessing that there are 500 tails - it won't be 100% assurance, but it'll be far better than 50%.

 

In the insurance industry, there are more complex patterns, but actuaries can still make predictions using the Law of Large Numbers. For instance, while it is true that some individuals who smoke live to a ripe old age (George Burns famously smoked his trademark cigars until he died at age 100), taken overall, there is a statistical pattern that smoking results in a shorter life span, and increases the risk of certain kinds of cancers, among other things.

 

That's life insurance. For people who buy car insurance, there is the "high risk" drivers who are male and between 18 and 25 years old. This isn't saying that all drivers in that category are high risk, but the Low of Large Numbers says that taken as a whole, it's that category that is most likely to drive unsafely and cause large amounts of health and property damage.

The Law of Large Numbers is the principal that backstops much of statistical work. It states that as the number of experiments or trials with the same likelihood grows, the results will become increasingly orderly and follow a pattern.