From 1940s to 1950s, Thomas Simpson made a rate table that increased with the increase of mortality according to Hurley's life table, and James dodson found a method to calculate insurance premium according to factors such as age difference. The emergence of actuarial science is marked by the world's first life table published by British astronomer Harley, the discoverer of Halley's comet, in 1693, which has a history of more than 300 years.
Since the 20th century, the situation has changed fundamentally. First of all, there are unprecedented risks; Secondly, in the increasingly perfect insurance market, the competition among insurance companies is becoming more and more fierce; Furthermore, there are many factors, such as the sharp drop in insurance rates, the pursuit of customer first, and even the government's control over certain insurance rates. Therefore, it is no longer possible for contemporary insurance companies to charge premiums significantly higher than the appropriate level and continue to operate.
With the development of statistical theory, insurance companies try to use more accurate methods to replace previous empirical judgments when determining insurance rates, unexpected loss reserves, retention limits, unexpired liability reserves and outstanding claims reserves. The original definition of actuarial science is "to determine how much insurance premium an insurance company should charge by estimating the probability of loss accidents such as fire, theft and personal death."
In actuarial science of life insurance, the calculation of interest rate and mortality rate are two basic problems to determine the cost of life insurance. Because interest rate is generally controlled by the state, interest rate has not been the main concern of insurance actuaries for a long time. The calculation of mortality rate, that is, the establishment of life table, has become the core work of life actuaries and is still the subject of actuarial research.
Non-life insurance actuaries always pay attention to the frequency, scale and control of losses. Non-life insurance actuarial has developed two important branches: one is loss distribution theory; The second is risk theory.
With the deepening of the marketization of financial interest rate, the risk of insurance funds has also become the core issue of actuarial research. The problems to be studied in this aspect include sensitivity analysis and portfolio analysis of investment income, asset-liability matching and so on. The most basic principles of actuarial science can be simply summarized as the principle of balance of payments and the law of large numbers.
The so-called balance principle is to make the cash value of pure premium income equal to the cash value of insurance payment during the insurance period. Because of the long-term nature of life insurance, the interest rate factor should be considered in the calculation. There are three different calculation methods: ① According to the difference between the principal and interest sum (final value) of premium income at the end of insurance period and the principal and interest sum (final value) of paid insurance premium; ② Calculated according to the fact that the present value of premium income is equal to the present value of insurance payment when the insurance contract is established; (3) The premium income at some other time point is equal to the sum of principal and interest or the present value of insurance payment.
Law of large numbers: a series of theorems that show the inevitable quantitative laws of a large number of random phenomena (events) due to the mutual cancellation of contingency. There are three common laws of large numbers:
Chechshev's law of large numbers
Bermuli's law of large numbers
The development of Poisson's law of large numbers is inseparable from actuaries. With the development of insurance industry and the establishment of strict mathematical foundation, the requirement of insurance premium rate for calculation is very high, so actuaries came into being. Actuaries are mathematical professionals employed by insurance companies, mainly engaged in the calculation of insurance premiums, compensation reserves, dividends, insurance coverage, pensions, annuities and so on. The calculation basis comes from the claim reference table, which is based on the experience and relevant statistical data of the company and its peers.