## Study on the trend of mortality rate and measurement of longevity risk in China

(2.Chinese Academy of Labor and Social Security)

(3.School of Statistics, Renmin University of China)

**【Abstract】**Using the statistics of mortality rate from 1950 to 2018, this paper studies the trend of mortality rate in China, and establishes a stochastic mortality model to measure the longevity risk faced by China’s pension system. The results are as follows. (1) China’s crude mortality rate declined rapidly from 1950 to 1981. The pace of decline increased first, then decreased with age, and there is little difference in gender. (2) China’s crude mortality rate declined steadily from 1981 to 2005. The rate of reduction in infant mortality has increased greatly, and that for the males aged 15–59 has slowed down significantly, which has resulted in a lagged-behind life expectancy for males as compared with females. (3)From 2005 to 2015, the crude mortality rate increased, which is resulted from the changes in population age structure. Meanwhile, the age-specific mortality rate still maintained a downward trend. The mortality rate of the population over 60 years old declined faster than before. (4) In population mortality prediction, the robust model takes the trend of mortality change into consideration, and hence enhances the validity of prediction. (5) The robust model has lower modeled risk in measuring longevity risk and is more conservative in longevity risk estimation. Results from this model can retain more risk reserve for the pension system.

**【Keywords】 **population mortality; trend; longevity risk; measurement model;

**【DOI】**

(Translated by DUAN yinhong)

**Footnote**

[1]. ① Since the age effect factor uses the concept of change from the last period in statistics, a geometric average method should be used to characterize the average decline in mortality over a period of time. This indicator is used by the North American Society of Actuaries, which is applicable to data with fewer years can be obtained. The average annual change rate of mortality over a certain period of time can be calculated, and the comparability is strong. [^Back]

[2].
② The United Nations World Population Division publishes *World Population Prospects: The 2017 Revision*every two years, and uses Bayesian stratified model methods to estimate the age-specific mortality data of countries in the world. The method is scientific, the results are reasonable, and it has certain authority in the world. It has strong reference value for this study.
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[3].
① The population mortality rate generally shows a downward trend with time, so In [*m* (*x*, *t* + 1) / *m* (*x*, *t*)] is a negative value. After adding the minus sign, it is used as an approximation of the relative level of mortality reduction.
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[4]. ② The Chinese male population mortality rate is selected as the representative of the study because the population change sampling is used in most years, and the female population mortality rate is significantly lower than that of males. For some ages, females have zero death, which leads to distortion of mortality rates. It is less common for male population. [^Back]

[5]. ① In 2015, the infant mortality rates in the United States, Sweden, and Japan were 6.394‰, 2.785‰, and 2.080‰, respectively; in 1985, the average age fractions of the adult population in the United States, Sweden, and Japan were 5.108‰, 3.621‰, and 3.306‰. [^Back]

[6]. ① For the mortality prediction of the population aged 100 years old or above, extrapolation can performed by the mortality model of the elderly population, such as Gompertz model. [^Back]

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ISSN:1000-7881

CN: 11-1043/C

Vol , No. 03, Pages 67-79+127

June 2019

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