Collectivised Pension Investment

We study the optimal management of a collectivised pension fund, where all investors agree that the assets of deceased members are shared among the survivors. We find that for realistic parameters based on the UK pensions market, a collectivised fund achieves an approximately 20% better return than either an annuity or a personal investment fund. We introduce models of investor preferences over a stream of pension payments in the presence of mortality, incorporating a new concept of adequacy. We find that for risk-averse individuals, pension adequacy plays an important role in determining the optimal fund management strategy. A key issue in the design of collective funds is how to ensure the fund treats all investors fairly. This is a trivial problem in the case that all investors have identical preferences, wealth and mortality, but becomes challenging for heterogeneous funds. We give a strategy for the management of heterogeneous funds in complete markets and prove that it is asymptotically optimal in the absence of systematic longevity risk.