Fundamentals of Actuarial Mathematics, 3rd Edition

11 Multiple-decrement theory

11.1 Introduction

Our discussion of insurance contracts up to now has been concerned with benefits payable upon the occurrence of death. We now investigate situations when an insured is at the same time subject to several different events that can have financial impact.

One example, which we mentioned earlier, is the event of withdrawal or lapse, whereby an insured life terminates the contract and receives a cash value. To properly model a life insurance contract, one must consider two causes of termination, death and withdrawal, operating simultaneously.

Sometimes the insurer must distinguish between different causes of death. For example, some policies have a feature that provides additional death benefits for accidental death as opposed to death from natural causes.

Some policies include disability benefits, providing income for people who can no longer work. For such, the insurer must consider the possibility of disability, as well as death and withdrawal.

For employees covered under a pension plan, there are at least four events of interest: disability; death; termination of employment; and retirement.

These are just a few of the possibilities, and many more can arise. In this chapter we analyze the general situation.

11.2 The basic model

We suppose that we have m different causes of failure operating simultaneously on a group of lives. These causes are often referred to as decrements, since they bring about a decrease in the number of lives ...