Heterogeneity-adjusted management of pension funds using adaptive representative agents

This paper focuses on defined-benefit pension funds in which heterogeneous plan members differ in age, salary, contribution rate, and other characteristics. The co-variation of these characteristics proves to have an important effect on the management of the fund. For example, we find that members’ ages and salary growths, if co-vary in unfavourable way, can substantially increase the funds’ liability, which in turn drives up the amount of funding required and the proportion of risky investment. This coupling effect of heterogeneity is demonstrated first through analytical statements which we derive under a simplified assumption of no investment constraints. In constrained cases for which analytical solutions are unavailable, we develop a numerical method that finds the heterogeneity-adjusted management decisions using a so-called adaptive representative agent (ARA), whose characterization is given explicitly in a key theorem. Whereas traditional methods often suffer from numerical complexity that grows exponentially with the number of heterogeneous members, the computational cost of the proposed ARA method is only linear in the number of time steps. This advantage of the ARA method and its ability to rectify the coupling effects of heterogeneity are demonstrated through our numerical example.