R Programming for Actuarial Science

17 Approaches to Fitting Mortality Models: The Markov 2-state Model and an Introduction to Splines

Peter McQuire

library(stats4)
library(splines)

17.1 Introduction

In the previous chapter we discussed the relationship between the mortality rate, , and the survival probability, . This led to a general expression for the likelihood of our data. Furthermore, by assuming that the mortality rate was constant over a chosen age range, we obtained an expression for the “crude rate”, , for that range. These crude rates represent the maximum likelihood estimates of the constant mortality rates over the chosen age range.

However, if we are to make the a priori assumption that mortality rates should increase smoothly between successive ages, there is a problem with these crude rates. The inherent uncertainty, or stochastic error, will result in crude rates which are higher than the true rates at some ages, and lower at other ages. Figure 17.1 is a plot of crude rates we shall analyse later in the chapter; we can see that there are many instances where we would want to improve on the crude rates, particularly when our population size is smaller e.g. at older ages. For example, at ages 27 ...