Optimal post-retirement investment and consumption under longevity risk in collective funds

We study the optimal investment-consumption problem for a homogeneous collective of n individuals subject to longevity risk with Epstein–Zin preferences. Our focus is on longevity risk, so for simplicity, we use the Black–Scholes model for assets. We compute analytic formulae for the optimal investment strategy when consumption is in discrete time and there is no systematic longevity risk. We develop a stylized model of systematic longevity risk in continuous time, which allows us to obtain an analytic solution to the optimal investment problem in this case. We numerically solve the same problem using a continuous-time version of the Cairns–Blake–Dowd model, a mortality model for describing systematic longevity risk. We apply our results to estimate the potential benefits of pooling longevity risk over purchasing an insurance product such as an annuity, estimate the impact of systematic longevity risk on initial fund requirements, and to estimate the benefits of optimal longevity-risk pooling in a small heterogeneous fund.