Pareto optimal pension risk allocations

We consider a funded pension system where collective risks, in a simple Black-Scholes financial market, are allocated to the retirement savings of individual participants. In particular, we consider an allocation in such a way that the relative effect on total retirement wealth, that is, the sum of financial wealth and human capital, is the same for each participant. We show that this allocation is Pareto efficient. This stylized life-cycle fact inspired the new Dutch retirement system. Subsequently, we extend the allocation rule to a setting that includes annuity risk. This risk can be a traded risk (e.g., interest rate risk) as well as a non-traded risk (e.g., longevity risk). From our closed-form solutions, we identify the similarities between our optimal allocation rule and the allocation rule in the new Dutch retirement system. A numerical example illustrates our findings.