Practical analysis of a pooled annuity fund with integrated bequest

A pooled annuity fund with an integrated bequest, introduced by Bernhardt and Donnelly (2019), is investigated for a finite pool of participants. In this fund, participants each receive an income while they are alive and a bequest payment upon their death, in exchange for paying their pension savings into the fund when they join.
The fund is placed in a discrete-time setting in this paper and the expected present value of a regular payment for life from the fund is derived. Using this annuity value, a numerical simulation is done of the fund under a stochastic mortality model. Each year, a new group of people join the fund, each bringing the same amount of money and with lives assumed to be independent random variables.
It is found that the distribution of income paid to each cohort varies, with the last cohort having the widest income distribution when they are old. Around 100 participants are needed to join every year to gain most of the benefits of pooling longevity risk, based on the model used for the simulations. These results hold whether there is a bequest or not in the fund.
The results show that a bequest could be integrated into pooled annuity fund, and still pay a table income, albeit at a cost of a lower income compared to the fund without a bequest.