Asymptotically Optimal Management of Heterogeneous Collectivised Investment Funds

TL;DR

This paper develops an axiomatic framework for managing heterogeneous collectivised investment funds, providing strategies that asymptotically maximize utility for large investor populations under specific market assumptions.

Contribution

It introduces an axiomatic approach to manage heterogeneous funds and derives strategies that achieve optimal utility bounds asymptotically.

Findings

Provides an upper utility bound for investors in heterogeneous funds.

Proposes management strategies that asymptotically reach this bound as investor number grows.

Assumes complete markets and no systematic longevity risk.

Abstract

A collectivised fund is a proposed form of pension investment, in which all investors agree that any funds associated with deceased members should be split among survivors. For this to be a viable financial product, it is necessary to know how to manage the fund even when it is heterogeneous: that is when different investors have different preferences, wealth and mortality. There is no obvious way to define a single objective for a heterogeneous fund, so this is not an optimal control problem. In lieu of an objective function, we take an axiomatic approach. Subject to our axioms on the management of the fund, we find an upper bound on the utility that can be achieved for each investor, assuming a complete markets and the absence of systematic longevity risk. We give a strategy for the management of such heterogeneous funds which achieves this bound asymptotically as the number of investors tends to infinity.