Fundamentals of Actuarial Mathematics, 3rd Edition

4 Life annuities

4.1 Introduction

The financial losses that we listed at the beginning of Chapter 1 are no doubt familiar to all readers. Another type of risk, which may not be so obvious, is that of living too long. Given our definition of risk as the possibility of something bad happening, the reader may wonder about this statement. After all, is not living a long life a good rather than bad occurrence? It certainly can be, but it does carry with it the possibility of financial hardship if one does not have adequate income. Imagine the decision faced by a retired individual who has accumulated savings of 1 000 000, which is invested at an annual rate of 5%, providing an annual income of 50 000. Imagine also that the individual decides that this is an insufficient return, so it is necessary to consume a portion of the capital each year, as well as the interest. Doing so, however, runs the risk that the entire capital may be depleted before death, leaving the individual with no source of income for his/her remaining lifetime.

Life annuities are a means of insuring against such a risk. A life annuity is a contract between an insurance company, known as the insurer, and another party, known as the annuitant, which provides the following. In return for the payment by the annuitant of prescribed premiums, the insurer will provide a sequence of payments, known as annuity benefits of prescribed amounts and at prescribed times. The unique provision is that the annuitant must be alive ...