a b s t r a c tThe aim of this paper is to design an automatic balancing mechanism to restore the sustainability of a pay-as-you-go (PAYG) pension system based on changes in its main variables, such as the contribution rate, normal retirement age and indexation of pensions. Using nonlinear optimisation, this mechanism, identifies and applies an optimal path of these variables to a PAYG system in the long run and absorbs fluctuations in longevity, fertility rates, salary growth or any other events in a pension system.

The aim of this paper was to design optimal strategies using nonlinear dynamic programming to guarantee the required level of liquidity in pay‐as‐you‐go pension systems through changes in the key variables of the system, such as the contribution rate, retirement age and/or indexation of pensions. These strategies, also known as automatic balancing mechanisms (ABMs), calculate the optimal path of these variables over time, managing fluctuations in longevity, fertility rates, salary growth or any other kind of uncertainty faced by the pension scheme without repeated legislative intervention. A numerical application of our model, which uses the projection of the population structure of two representative countries, illustrates the main findings of the paper. Copyright © 2015 John Wiley & Sons, Ltd.

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State pension systems are usually pay-as-you-go financed, i.e. current contributions cover pension expenditure. However, some countries combine funding and pay-as-you-go (PAYG) elements within the first pillar. The aim of this paper is twofold. First, using nonlinear optimisation based on Godínez-Olivares, Boado-Penas, and Haberman (2016), it seeks to assess the impact of a compulsory funded defined contribution (DC) pension scheme that complements the traditional defined benefit (DB) PAYG on the level of pension benefits. Future expected returns for both the funded part and the buffer fund of the PAYG are simulated through the non-overlapping block bootstrap technique. Second, in the case of a partial financial sustainability, we design different optimal strategies, that involve variables such as the contribution rate, age of retirement and indexation of pensions, to restore the long-term financial equilibrium of the system. We show that the adjustments needed to ensure sustainability for the mixed pension systems are less severe that the pure DB PAYG but the total replacement rate for the former is lower in most of the cases studied. When calculating the return that the individuals would receive, we prove that some cohorts are better off under a mixed pension system.

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