OPTIMAL MIX BETWEEN PAY AS YOU GO AND FUNDING FOR PENSION LIABILITIES IN A STOCHASTIC FRAMEWORK

This paper addresses the financing of public pensions in a stochastic environment.
Traditionally, funded and unfunded pension schemes have been viewed as
opposite solutions for the first pillar of public pensions. However, more recently
countries as Sweden and Poland have explored mixed solutions that combine
pay-as-you-go (PAYG) with funding mechanisms. The aims of this paper are
to examine the rationality of such a combination using portfolio theory arguments
and to find the optimal split of the contributions between the two systems.
We first introduce the classical deterministic model leading to the well-known
Samuelson–Aaron rule according to which diversification is never optimal. We
then introduce different stochastic models in which the main processes (wage
growth, population growth, financial rate of return) are random. In particular,
we obtain conditions on parameters to justify diversification and explicit optimal
sharing between PAYG and funding. We also introduce the possibility of
investing in several financial assets and explore the impact of introducing systematic
longevity risk.