by paying the premium, the insured transfers the risks faced by individuals or families to the insurance company, and when the insured or the insured suffers losses, the insurance company provides corresponding economic compensation. It is a risk-bearing way to compensate the losses of a few people in the uncertain future by paying the premiums by most people.

the insurance company will invest the premium and provide the insured with a fund, which must be enough to cover the losses suffered by the insured, that is to say, the fund must have enough funds to pay all the compensation amounts incurred during the insurance period. Therefore, insurance companies need to accurately predict the loss probability of risk groups through scientific methods, that is, the law of large numbers, in order to maintain the stability of the company's operation.

1. what is the law of large numbers?

the law of large numbers, also known as the law of large numbers, is a law that describes the probabilistic nature when the number of experiments is large. In the repeated occurrence of a large number of random events, there is often an almost inevitable law, which is the law of large numbers. In layman's terms, the frequency of random events is close to its probability when the experiment is repeated many times under the same condition.

The classic example of the law of large numbers is coin toss. If you toss a coin once, the probability of the coin landing with the heads and tails facing up is 5% respectively, that is, 1:1. If you toss it twice, it is difficult to get the same result. If you toss it 1 times, you still can't ensure that you get the same result with the heads and tails facing up. However, when you keep throwing it for thousands or even tens of thousands of times, we will find that the number of heads or tails will be close to half. The more times you throw coins, the more likely it is that the ratio of heads and tails will be close to equal, and similar things are throwing screens.

the law of large numbers of insurance, also known as the principle of large number of risks, the law of large numbers and the law of average, is an almost inevitable law that people have found in long-term practice and often appear in a large number of repetitions of random phenomena.

second, the application of the law of large numbers in insurance

insurable risks need to meet a series of conditions, two of which are that the losses are measurable and there are a large number of insured objects with homogeneous risks.

The loss is estimated by the law of large numbers and probability statistics: by observing a large number of risk units in the insurance collection, the probability of loss is estimated; With the increase in the number of risk units in the insurance collection, it is possible to estimate the loss more accurately and determine a more reasonable premium.

Insurance companies collect specific information of many individuals to determine their loss patterns. For example, life insurance companies have always recorded the number of insured people who have died by gender and their age at the time of death. Insurance companies will also record the age of death of people of different sexes in the general population by consulting relevant general population records. Using these statistical records, insurance companies can compile a life table, that is, a table listing the number of people who may die at each age in a large population. The life table lists the mortality rate, which is the mortality rate of a specific population in a specific time. Insurance companies have also compiled a similar table, called the incidence table, which lists the incidence of specific groups by age. By applying accurate life tables and incidence tables, insurance companies can predict the possible loss rate of specific insured groups. Insurance companies use these predicted loss rates to determine insurance rates that are sufficient to pay the claim amount.

third, the law of large numbers in the era of big data

with the rise of new technologies such as big data, internet of things and artificial intelligence in recent years, the means of accurately identifying risks are more diverse and the predictability of risks is getting higher and higher. There is even a view in the industry that the "law of large numbers" has failed. Then, is there a contradiction between the "law of large numbers" of insurance and the accurate identification of risks? How to balance the relationship between accurate pricing and loss?

the reasons why the industry thinks that the importance of the law of large numbers is gradually decreasing are mainly reflected in the following aspects: first, the fairness of insurance pricing is challenged; second, the law of large numbers is challenged as a probability measurement method; and third, personalized demand has become an important development model and driving force of the industry.

however, the "law of large numbers" is not contradictory to accurate pricing.

first of all, it usually takes a huge cost to accurately determine individual characteristics, including individual risks. The law of large numbers actually provides a means for the insurance industry to measure objective risks. In the era of big data, the insurance industry should seek accurate pricing and create personalized insurance business based on the law of large numbers and new technologies.

Secondly, the current risk measurement technology is not accurate enough to the point where the law of large numbers is invalid, that is to say, everyone's risk cannot be measured yet, so the law of large numbers is still effective. Wei Li, director of the Department of Insurance at Renmin University of China, believes that it will be fairer for the insured to be able to make differential pricing by risk classification. Technological progress can't change the objectivity of risk, and accurate risk identification and pricing is to share losses more fairly.

Thirdly, scientific and technological progress has expanded the business field of insurance institutions and enhanced the importance of insurance industry in various risk management systems. "With the rapid progress of science and technology, the means of accurately identifying risks has also promoted people's awareness of risks and seen the inadequacy or inefficiency of self-management, thus increasing the demand for insurance." Wang Xiangnan, deputy director of the Insurance and Economic Development Research Center of China Academy of Social Sciences, believes that many types of accidents have been effectively controlled at present, but other types of accidents have gradually emerged with the changes of social production and lifestyle, such as network security incidents, public health incidents and social security incidents.