Fundamentals of Actuarial Mathematics, 3rd Edition

3 The life table

3.1 Basic definitions

For the actuary working in the life insurance field, a major objective is to estimate the mortality pattern which will be exhibited by a group of individuals. A basic device for accomplishing this is known as a life table. (It is also known as a mortality table – an interesting example of a word and its opposite being used interchangeably.)

Let ℓ₀ be an arbitrary number, usually taken to be a round figure such as 100 000. Suppose we start with a group of ℓ₀ newly born lives. We would like to predict how many of these individuals will still be alive at any given time in the future. Of course, we cannot expect to compute this exactly, but we can hope to arrive at a close estimate if we have sufficiently good statistics. In the first part of this book we will make the assumption that we can indeed arrive at exact figures. This is in keeping with the concept of a deterministic model introduced in Chapter 1. In Part II, we introduce the stochastic model for mortality, where we investigate the more realistic assumption that the quantities we want are random variables. Let ℓ_x be the number of those original lives aged 0 who will still be alive at age x, and let d_x be the number of those original lives aged 0 who die between the ages of x and x + 1. The basic relationship between these quantities is

(3.1)

A life table is a tabulation of ℓ_x and ...