16 The Markov 2-State Mortality Model
Peter McQuire
16.1 Introduction
One of the fundamental tasks of the actuary who works in the life assurance or pension fields is to estimate the mortality characteristics of a policyholder or pension scheme member. For example, actuaries will be required to estimate the probability that a life which has taken out a pure endowment policy will survive to the end of the policy and be entitled to the payment. In the case of a pension scheme member, actuaries must estimate the probability that lives will survive successive future years when pension payments will be made.
(Please also see Chapter 22 which discusses more general multiple state Markov models; the model covered in this chapter is the simplest example of such a model.)
16.2 Markov 2-State Model
Many models have been developed to estimate these probabilities, the most fundamental of which is arguably the single decrement 2-state “alive-dead” Markov model (“2-state Markov model”), which is the subject of this chapter. In this model, lives can be in one of two states, alive (
) or dead (
), at time
, and transition at any time from state to state at the rate of per unit time. (Note that ...