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Law of Large Numbers

Insurance companies use the law of large numbers to estimate the losses a certain group of insureds may have in the future. For example, using statistics, an Actuary looks at losses that have occurred in the past and predicts that in the future approximately two out of 100 policyholders will have a claim. Thus, if the company writes 100 automobile policies, it may expect to pay two claims. This is referred to as loss frequency.

Insurers must also determine the average cost of claims over time, or loss severity. If the average claim resulted in the company paying $1,000, then the Actuary will predict that total losses for the upcoming year will be $2,000 (two claims at $1,000 each).

The law of large numbers states that as the number of policyholders increases, the more confident the insurance company is its prediction will prove true. Therefore, they attempt to acquire a large number of similar policyholders who all contribute to a fund which will pay the losses.

This example may help you better understand how the law of large numbers relates to insurance:

Suppose you had a standard deck of cards containing 52 cards, 13 in each suit.

  • What are the chances that you could pick one card and pull out the ace of spades?

Its one in 52, because there is only one such card in the deck.

If someone told you hed give you $100,000 if you could pick the ace of spades with a single draw, but that you would owe him $100,000 if it was not there, would you take that bet?

  • What if the person said you could draw four times?  Ten times?

  • Would you be more confident if you knew you could improve your odds by making more draws?

Insurance is similar. The insurer may know that on average two out of 100 homes will burn in a given year, but it will be much more confident in this prediction if they insure 1,000 homes even more confident if it insures 100,000 homes. The more chances you get, the more likely you will achieve the desired outcome.