2020/04/02 by John Armstrong, Armstrong, John, Cristin Buescu +1
Decision Sciences · Economics, Econometrics and Finance · #FOS: Economics and business #Financial Markets and Investment Strategies #Portfolio Management (q-fin.PM) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2004.01506
openalex publication_date 2020/04/02 · openalex created_date 2020/04/10 · openalex updated_date 2026/07/28
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.