  We quantify the benefit of collectivised investment funds, in which the
assets of members who die are shared among the survivors. For our model, with
realistic parameter choices, an annuity or individual fund requires
approximately 20\% more initial capital to provide as good an outcome as a
collectivised investment fund. We demonstrate the importance of the new concept
of pension adequacy in defining investor preferences and determining optimal
fund management. We show how to manage heterogeneous funds of investors with
diverse needs. Our framework can be applied to existing pension products, such
as Collective Defined Contribution schemes.
