This volume addresses the most important issues of the ongoing discussion on designing social security. It provides fundamental results for pay-as-you-go social security, covers the issues of social security during demographic transition and examines the inclusion of risk aspects into the analysis of social security. An empirical case study of Germany yields the surprising result that de facto the German public pension scheme already comprises an implicit demographic factor. This book allows a subtle understanding of how interacting risks are treated within different pension systems and thereby provides a basis for the development of innovative ways of risk sharing.