This chapter contains some extended mortality and statistics tables that were referred to throughout the book.

Tables 14.1 and 14.3 are mortality tables listing qx values, male and female, for ages 50–120; Table 14.2 offers an international comparison of qx values at age 65.

Note the difference between the “annuitant” mortality Table 14.1 and the “insurance” mortality Table 14.3. For the most part, the qx rates at any fixed age are lower in a mortality table that is used for pricing and valuing pension annuities than in the table used for life insurance. This difference is due to adverse selection—healthier individuals tend to purchase pension annuities rather than life insurance. Of course, individuals who have actually qualified for life insurance might be relatively healthier than those who simply wanted to purchase life insurance but did not qualify. For more information about what actuaries call “ultimate” and “select” mortality tables, see Bowers et al. (1997).

Table 14.4 provides values for the CDF of the normal distribution under a zero mean (µ) and standard deviation of sigma (σ). If you want to compute the probability Pr[X ≤ x] under a nonzero µ, then use the numbers given x – µ. For example, with µ = 0 and σ = 20% we have Pr[X ≤ 10%] = 69.15%, but when µ = 5% we have Pr[X ≤ 10%] = 59.87%. Intuitively, increasing the mean should reduce the probability of earning less than any given threshold.