A Simple Two Period Overlapping Generation (OLG) Model For Public Pension Scheme (PAYG)

In this paper, we develop in a PAYG public pension system, various ways to share the longevity risk across generations of active affiliates and retirees. We consider a simplified two period Overlapping generation (OLG) model with three major groups: active workers, new retirees and existing retirees. Two levels of risk sharing are proposed; in a first step we develop the sharing between the contributors and the beneficiaries by proposing various designs of the plan, from Defined Benefit to Defined Contribution including hybrid solutions such as Musgrave plans. For this level, the driving force is the dependency ratio. In a second step we consider the sharing between the retirees themselves by considering two important degrees of freedom: the level of the first pension for the new retirees and the revaluation of existing pensions for the older retirees. Different strategies of risk sharing are presented in this framework. We illustrate the concepts by numerical illustrations based on deterministic and stochastic demographic models