Pay-as-you-go pension systems: Automatic balancing mechanism based on nonlinear programming to restore the sustainability Humberto God´ ınez-Olivares ∗, † , Mar´ ıa del Carmen Boado-Penas ∗ and Steven Haberman ‡ March 31, 2015 Abstract The aim of this paper is to design an automatic balancing mechanism to restore the sustainability and liquidity of a Pay-As-You-Go pension (PAYGO) system, based on minimising changes in the main variables, such as the contribution rate, nor- mal retirement age and indexation of pensions. This mechanism, that uses nonlin- ear optimisation, identifies and applies an optimal path of these variables into a PAYGO system in the long run and absorbs fluctuations in longevity, fertility rates, life expectancy, salary growth or any other random events in a pension system. JEL Classification: E62, H55, J11, J26 Keywords: Liquidity, Optimisation, Pay-as-you-go, Public pensions, Risk, Sus- tainability. * Institute for Financial and Actuarial Mathematics (IFAM), Department of Mathematical Sciences, Uni- versity of Liverpool, Mathematical Sciences Building, Liverpool L69 7ZL, United Kingdom. (email: hgodinez@liv.ac.uk, carmen.boado@liverpool.ac.uk. Tel:+44-151-794-4026). † Corresponding author. ‡ Faculty of Actuarial Science and Insurance, Cass Business School, City University, Bunhill Row, Lon- don, United Kingdom. (e-mail: s.haberman@city.ac.uk). 1