Notations used in Actuarial Tables

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31 Jul 2018, 18:34

There are basically 4 notations -
  • lx: It is the number of surviving lives alive at exact age ๐‘ฅ.
  • ๐‘‘๐‘ฅ: It is the number of deaths over the year of age ๐‘ฅ.
  • qx: Probability of dying in year x
  • px: Probability of surviving year x
Now there are 4 relations that helps in understanding the tables-

1. l๐‘ฅ+1=๐‘™๐‘ฅโˆ’๐‘‘๐‘ฅ: It means the number of surviving person at age x+1 is equal to the number of surviving person at age x minus total deaths in year x

2. ๐‘ž๐‘ฅ=๐‘‘๐‘ฅ/๐‘™๐‘ฅ: It means the number of deaths in a year divided by number of person living at age x

3. ๐‘๐‘ฅ=(๐‘™๐‘ฅ+1)/lx: It means the probability of survivingย  is equal to the number of people alive in year x +1 divided by the number of people died in the year x

4. px = 1-qx: It means that the probability of surviving is equal to 1 minus probability of death. In other words, the probability of surviving and probability of death equals 1

Collectively, ๐‘™๐‘ฅ, ๐‘‘๐‘ฅ, ๐‘ž๐‘ฅ and ๐‘๐‘ฅ form what is called a โ€œlife tableโ€ or โ€œactuarial tableโ€.ย ย 

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