Life Insurance Basic Principles (Part IV) - The Law of Large Numbers

The Basic Principles of Life Insurance (Part IV)

The Law Of Large Numbers

For a plan of insurance to function, the pricing method needs to measure the risk of loss and determine the amount to be contributed to the pool by each participant. The theory of probability provides such a scientific measurement.

Probabilities for life insurance are represented in a mortality table. The mortality table is very versatile, developing probabilities of dying over the entire life span. Life expectancy at any age is the average number of years of life remaining once a person has attained a specific age. It is the average future lifetime for a representative group of people at any given age. The probable future lifetime of any individual, of course, will depend on his or her state of health, among other things, and may be much longer or shorter than the average.

The statistical group that is observed for purposes of measuring probability must have mass—that is, the sample must be large enough to allow the true underlying probability to emerge. The law of large numbers states that as the size of the sample (insured population) increases, the actual loss experience will more and more closely approximate the true underlying probability. This means that the insurer’s statistical group must be large enough to produce reliable results, and that the group actually insured must be large enough to produce results that are consistent with what probability predicts.

Insurance relies on the law of large numbers to minimize the speculative element and reduce volatile fluctuations in year-to-year losses. The greater the number of exposures (lives insured) to a peril (cause of loss/death), the less the observed loss experience (actual results) will deviate from expected loss experience (probabilities). Uncertainty diminishes and predictability increases as the number of exposure units increases. It would be a gamble to insure one life, but insuring 500,000 similar persons will result in death rates that will vary little from the expected.

A peril is a cause of a loss. In life insurance, the event against which protection is granted, death, is uncertain for any one year, but the probability of death increases with age until it becomes a certainty. If a life insurance policy is to protect an insured during his or her entire life, an adequate fund must be accumulated to meet a claim that is certain to occur.

Some people claim that insurance is a gamble. Insurance is actually the opposite of gambling. Gambling creates risk where none existed. Insurance transfers an already existing risk exposure and, through the pooling of similar loss exposures, reduces financial risk.