R Programming for Actuarial Science

22 Markov Multiple State Models: Applications to Life Contingencies

Peter McQuire

library(markovchain)
library(expm)

22.1 Introduction

Markov models are extensively used in actuarial work where we need to develop an understanding of how the state of a system may change in the future. The simplest Markov model actuaries will be familiar with is the “alive-dead” 2-state model discussed in Chapter 16, used to estimate probabilities that lives occupy these states at future points in time. In this chapter we develop this idea by looking at multiple-state systems.

Indeed, the focus of this chapter is the “Healthy-Sick-Dead” model, introduced in Section 22.5.2, and the related material which follows; such a model may be important to assess the length of time a policyholder or employee may be deemed as “sick” or in ill-health. Another example of a multiple state model in an actuarial context is that which models the state of a pension scheme member; they may be a contributing member, a member who has ceased to pay contributions but is not yet in receipt of a pension, or may be in receipt of this pension. They may also have transferred to an alternative arrangement or have died. By understanding the various probabilities of existing in particular states and of particular transitions occurring between states, we can better understand the expected future cashflows.

The chapter includes a section on Markov chain models, before developing these ideas by looking at Markov jump models. The ...