An approach to the study of multiple state models

Abstract

1.1. Multiple state life tables can be considered a natural generalization of multiple decrement tables in the same way as the latter can be considered a natural generalization of the ordinary mortality table. The essential difference between a multiple state model and a multiple decrement model is that the former allows for transitions in both directions between at least two of the states, see for example Haberman (1983, Fig. 2). whereas in the latter, transitions between any pair of states can be in one direction only, if they are possible at all; see for example Haberman (1983, Fig. 1). Multiple state life tables, unlike mortality tables and multiple decrement tables, are not included in the professional actuarial examination syllabuses in Britain and have only rarely been mentioned in the British actuarial literature, one example being C.M.I.R. (1979, Appendix 2). Despite this, such models have been included in the actuarial examination syllabuses of other countries for several years, for example Denmark, and would appear to have obvious actuarial applications, for example sickness insurance. Dr Haberman's paper (J.I.A. 110) on the subject of multiple state models is to be welcomed since it provides both an introduction to this subject and an interesting application. The approach to the study of multiple state models put forward by Haberman (1983, §3) is characterized by the use of flow, orientation and integration equations. For brevity we shall refer to this as the FOI-approach to multiple state models. The purpose of the present paper is to put forward an alternative approach to multiple state models. This approach uses the forces of transition, or transition intensities, between states as the fundamental quantities of the model. For brevity we shall refer to this as the TI-approach.