Multi-life annuity products

Ermanno Pitacco

3.1 INTRODUCTION: FROM SINGLE-LIFE TO MULTI-LIFE ANNUITIES

The expression “multi-life annuity products” denotes contingent annuities that involve a group of individuals. At any point in time, the annuity payments depend on the current “status” of the group, ie, on which individuals out of the initial group as at the time of policy issue are alive.

The number of possible contingency arrangements depends on the initial size of the group, and may be huge if the group itself initially consists of many individuals. Nevertheless, a limited number of arrangements of practical interest can be singled out, notably if groups of two individuals are addressed.

Moving from single-life annuities to multi-life annuities, whatever the number of individuals may be, requires appropriate extensions of the actuarial structure.

In this chapter, we first present the biometric model, which can be used to express the random lifetimes of two individuals in quantitative terms. Following the logical structure of Chapter 2, we define expected present values (ie, actuarial values) of annuity benefits, which are then used for premium and reserves calculations. Numerical examples are provided for a

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