Fundamentals of Actuarial Mathematics, 3rd Edition

10 Multiple-life contracts

10.1 Introduction

In previous chapters we have studied insurance and annuity contracts sold to a single individual. There are many situations when such contracts are sold to a group of several people. We will concentrate on the case of two lives, the most common arrangement, which is sufficient to exhibit most of the complications.

The following are a few of the more usual situations. A married couple may wish to purchase an annuity that pays income while either of them is alive. They may also want an insurance policy that pays benefits on the second death, which in some jurisdictions enables them to pass on assets without paying estate taxes. Two business partners may desire a policy that pays a death benefit upon the first death of the two. A person may arrange for an annuity to be paid to a dependent, where payments begin only on the death of the supporting individual. We will discuss these and more in the following sections. For simplicity we assume aggregate mortality in this chapter. It is not too difficult to modify the results for the effects of selection.

10.2 The joint-life status

Consider a pair of lives, (x) and (y). Suppose that we consider the pair to be in a state of survival when both of them are alive. In other words, the pair fails on the first death. Such a pair is commonly known as a joint-life status. An annuity sold on a joint-life status would provide income as long as the status survived, that is, as long as both individuals ...