A simple formula for optimal management of individual pension accounts
This research considers optimal investment for an individual pension savings plan in receipt of gradual contributions against which one cannot borrow, using expected power utility as the optimality criterion.
It is well known that in the presence of credit constraints the Samuelson paradigm of investment in constant proportions out of total wealth (including current savings and future contributions) no longer applies. Instead, the optimal investment gives rise to so-called stochastic lifestyling, whereby for low levels of accumulated capital it is optimal to invest fully in stocks and then gradually switch to safer assets as the level of savings increases. In stochastic lifestyling not only does the leverage between risky and safe assets change but also the actual mix of the risky assets varies over time. While the existing literature relies on complex numerical computations to quantify optimal lifestyling the present paper provides a simple formula that captures the main essence of the lifestyling effect.
The proposed methodology has been successfully implemented by Allianz DSS – a pension savings provider in Slovakia.
The academic paper can be downloaded below, along with an accompanying summary document and a spreadsheet containing the Solver interface.