Zum Inhalt springen Zur Suche springen

08. Juli 2026

Some Mathematical Thoughts on PAYG Pension Schemes

Julia Eisenberg, Vienna University of Technology

Abstract:
Pay-as-you-go (PAYG) pension schemes are particularly vulnerable to demographic risks. This raises serious concerns about the long-term sustainability of public pension systems that rely on a PAYG financing model, where current contributions fund current pension expenditures. In this talk, we explore two potential approaches to reforming such systems.

The first approach assumes that any deficit in the PAYG scheme is immediately covered by the state. In return, individuals are required to invest a specified amount into a fund. This investment is structured such that individuals are expected, with a certain probability, to repay the state for the deficit incurred by the PAYG scheme. We compare the outcomes of this approach with those of the traditional direct contribution model and identify the conditions under which the proposed scheme would be advantageous.

The second scenario introduces a mixed pension framework (PAYG and funding) tailored for economies with a declining working-age population, operating under a defined benefit assumption. In this setup, we analyse the consequences of guaranteeing a zero return on the investments made in the funded component. Although this mixed system does not provide a hedge against demographic risks, it serves to delay the need for immediate
pension reforms.

Bio:
Julia Eisenberg is a professor of actuarial mathematics at TU Wien (Vienna University of Technology), Austria. She studied mathematics at the University of Duisburg-Essen and earned her PhD from the University of Cologne. In 2019, she completed her habilitation in applied mathematics, through an FWF Elise Richter project, on actuarial control problems under stochastic interest rates. Since 2021, she has been an Honorary Fellow at the University of Liverpool. Her research addresses insurance and pension systems, reinsurance, risk theory, dividend optimisation, and financial decision-making under uncertainty.