Between DB and DC: optimal hybrid PAYG pension schemes

In classical pension design, there are essentially two kinds of pension schemes: defined benefit (DB) or defined contribution (DC) plans. Each corresponds to a different philosophy of spreading risk between the stakeholders: in a DB the main risks are taken by the sponsor of the plan while in a DC the active members must bear all the risks. Especially when applied to social security pension systems, this traditional view can in both cases lead to unfair intergenerational equilibrium. The purpose of this paper, which focuses on social security, is twofold. First, we present alternative architectures based on a mix between DB and DC in order to achieve both financial sustainability and social adequacy. An example of this approach is the so-called Musgrave rule, but other risk-sharing approaches will be developed in a pay-as-you-go philosophy. More precisely, we build convex and log-convex families of hybrid pension schemes whose extremal points correspond to DB and DC. Second, we study these new architectures in a stochastic environment, and present different rules to select the most efficient ones. To do so, we search for optimality from a risk-sharing point of view among the new pension plans.