Optimal post-retirement investment under longevity risk in collective funds

TL;DR

This paper derives explicit formulas for optimal investment strategies in collective funds facing longevity risk, comparing pooling benefits to insurance solutions using analytical and numerical methods.

Contribution

It introduces analytic solutions for optimal investment under longevity risk in collective funds, including models with systematic risk and heterogeneous populations.

Findings

Pooling longevity risk can significantly improve investment outcomes.

Analytic formulas enable better understanding of optimal strategies.

Pooling benefits vary with heterogeneity and systematic risk presence.

Abstract

We study the optimal investment problem for a homogeneous collective of $n$ individuals investing in a Black-Scholes model subject to longevity risk with Epstein--Zin preferences. %and with preferences given by power utility. We compute analytic formulae for the optimal investment strategy, consumption is in discrete-time and there is no systematic longevity risk. We develop a stylised model of systematic longevity risk in continuous time which allows us to also 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. We apply our results to estimate the potential benefits of pooling longevity risk over purchasing an insurance product such as an annuity, and to estimate the benefits of optimal longevity risk pooling in a small heterogeneous fund.