Quantifying the trade-off between income stability and the number of members in a pooled annuity fund

TL;DR

This paper analyzes how the number of members in a pooled annuity fund affects income stability, deriving an analytical expression to quantify this relationship under fixed investment returns and systematic risk omission.

Contribution

It introduces an analytical approximation for the number of members needed to maintain income stability, independent of the mortality model, aiding fund management decisions.

Findings

Derived an analytical expression for income stability

Income stability depends on the number of members and fixed returns

The model is independent of the mortality assumptions

Abstract

The number of people who receive a stable income for life from a closed pooled annuity fund is studied. Income stability is defined as keeping the income within a specified tolerance of the initial income in a fixed proportion of future scenarios. The focus is on quantifying the effect of the number of members, which drives the level of idiosyncratic longevity risk in the fund, on the income stability. To do this, investment returns are held constant and systematic longevity risk is omitted. An analytical expression that closely approximates the number of fund members who receive a stable income is derived and is seen to be independent of the mortality model. An application of the result is to calculate the length of time for which the pooled annuity fund can provide the desired level of income stability