Mortality Compression and Longevity Risk. Jack C. Yue National Chengchi Univ. Sept. 26, 2009. Summary. Motivation What is Mortality Compression Measuring the Mortality Compression New Measurements and Results Discussions. Prolonging Life Expectancy.
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Jack C. Yue
National Chengchi Univ.
Sept. 26, 2009
For example, the life expectancies of U.S. male and female were at the upper 40’s in 1900’s and reached upper 70’s in 2000’s.
The life expectancies of Taiwan male and female have similar increasing trend.
National Health Insurance
Complete Life Table
Increments of Life Expectancy in Taiwan (Complete Life)
According to U.N., the world has an annual increment of 0.25 year, during the second half of 20th century. The trend is likely to continue, at least for a while.
In Taiwan, the life expectancies at age 65 were 10.62 and 13.25 years for the male and female, increased to 17.26 and 20.18 years, respectively. It increases about 50% more financial burden for retirement preparation.
Taiwan started national pension in 2008, in addition to other social insurance programs.
Stochastic mortality models are one of the popular choices to deal with the problem. Still, there is no guarantee if the future mortality will follow the historical trend.
Rectangularization of the survival curve
A state in which mortality from exogenous causes (e.g., infectious diseases) is eliminated and the remaining variability in the age at death is caused by genetic factors.
Premature deaths (including infants) will gradually decrease and some postulates that the distribution of death number will behave like a normal curve (at least for the part with age higher than the mode).
They applied the idea to complete life tables in Hong Kong (1976-2001) and found “the increase in human longevity is meeting some resistance.”
Note: The mortality rates of ages 85 to 120 were graduated using logistic curve.
Horizontalization: measure the descending speed at the mode
Verticalization: measure the descending speed at the mode
Longevity Extension: measure the expansion of lifespan
The elderly mortality rates are influenced the most.
The life expectancies, especially for the elderly, also are affected.
It is equivalent to using the mortality rates to explore the mortality compression.
Mode age (M) with the maximum # of deaths
The probability of pre-mature deaths
Shortest age interval covering certain prob.
Standard deviation 2 of normal distribution
Surviving beyond a high age, P(X > M + k)
We only have the values at integer and can use the 2-test (less powerful).
We can also apply the ratio
and this can be used to verify the normality.
Male and Female
Results computed up to age 100
We found that the mode age (& the life expectancy) continues to increase. The prob. of premature death and the shortest age interval of covering certain death prob. decrease.
But the standard deviation of death number and the prob. of survival beyond a high age do not show obvious signs of decrease.
The future life expectancy of most stochastic models will also increase. But there are not enough data for the old-aged group (e.g., oldest-old, 85+) and their mortality rates rely heavily on model assumption (such as extrapolation).
Question: Is Gompertz-type assumption feasible?
Mortality compression is not fully confirmed and the increase in human longevity is not meeting apparent resistance.
We are still not sure about the survival probability beyond very high ages.
For example, set the highest attained age to M + 2 (it is close to 100 years old currently). This would be plenty for most people and reduce the mortality risk for the insurance company.
Still, the need of people who outlive the age M + 2 is not satisfied.
The probability of survival beyond very high age (increasing as well) looks like a constant.
The highest attained age?
How do we obtain reliable estimates?
The mortality ratios? (Discount Sequence)