Dynamic reforming of a quasi pay-as-you-go social security system within a discrete stochastic multidimensional framework using optimal control methods

Athanasios A. Pantelous ¹   ; Alexandros A. Zimbidis ¹

¹ Department of Statistics Athens University of Economics and Business 76 Patision St. Athens GR-104 34, Greece

Applicationes Mathematicae, Tome 35 (2008) no. 2, pp. 121-144

Résumé

In many western economies, the phenomenon of ageing population implies that the large Pay-As-You-Go (PAYGO) social security system will run into several severe financial difficulties. In that direction, this paper constructs a discrete-time stochastic model for a quasi PAYGO social security system to allow the potential accumulation of a special (contingency) fund, which can oscillate so as to absorb fluctuations in the various system parameters involved. The basic difference equation is analytically designed including several control variables (i.e. different investment strategies, contribution rates, ages of eligibility for normal retirement and levels of pension benefits). The theoretical model is solved using standard linearization and stochastic optimization techniques resulting in analytic formulae for the control variables. These solutions are actually feedback mechanisms of the past fund values. Finally, we present a practical application for the projected population of Greece for the years 2007–2030 deriving a smooth solution for the development of the controls.

Détail

DOI : 10.4064/am35-2-1

Keywords: many western economies phenomenon ageing population implies large pay as you go paygo social security system run several severe financial difficulties direction paper constructs discrete time stochastic model quasi paygo social security system allow potential accumulation special contingency fund which oscillate absorb fluctuations various system parameters involved basic difference equation analytically designed including several control variables different investment strategies contribution rates ages eligibility normal retirement levels pension benefits theoretical model solved using standard linearization stochastic optimization techniques resulting analytic formulae control variables these solutions actually feedback mechanisms past fund values finally present practical application projected population greece years deriving smooth solution development controls