Cross-subsidy in life annuities

Ermanno Pitacco

10.1 INTRODUCTION: LOOKING AT TRANSFERS AMONG ANNUITANTS

Although all life contingency transactions can be analysed and quantified at an individual level (eg, in terms of the equivalence principle), in practice these transactions usually involve a group of individuals who transfer the same type of risk to an insurer. Of course, this is also the case for life annuity products, which have likewise previously been discussed in terms of a cohort of annuitants (see, for example, Sections 2.7.1 and 2.7.3 as regards the mutuality mechanism and its impact on the reserving process).

Owing to the existence of an annuitant population (a cohort, in particular), money transfers inside the population itself are possible, causing a cross-subsidy among the annuitants. The term “cross-subsidy” broadly refers to the effect of some arrangements adopted for sharing the cost of a set of benefits between the members of a given population. However, various types of cross-subsidy can be recognised, as sketched in Figure 10.1.

Mutuality, caused by the diversity of individual lifetimes, underpins the management of any life insurance or life annuity portfolio.

Conversely, other types of cross