"The main purpose of this paper is to analyze problems of financing an old-age insurance when birth rates are low and population declines or fertility fluctuates with time....[The author] investigates a theoretical model which analyzes the welfare optimal combination of private savings via the capital market and the state forced savings via a PAYG [pay-as-you-go] financed public pension system. Long-run effects as well as short-run implications are considered. The economic properties of an optimal steady state are determined and additionally an optimal transition path--the best feasible conversion policy--which leads to the new steady state is specified."