This study analyses the fiscal sustainability of the Finnish public sector using stochastic projections to describe uncertain future demographic trends and asset yields. While current tax rates are unlikely to yield sufficient tax revenue to finance public expenditure with an ageing population, if developments are as expected, the problem will not be very large. However, there is a small, but not negligible, probability that taxes will need to be raised dramatically, perhaps by over 5 percentage points. Such outcomes, if realised, could destabilise the entire welfare state. The study also analyses three policy options aimed at improving sustainability. Longevity adjustment of pension benefits and introduction of an NDC pension system would reduce the expected problem and narrow the sustainability gap distribution. Under the third option, pension funds would invest more in equities and expect to get higher returns. This policy also limits the sustainability problem, but only under precondition that policymakers in the future can live with substantially larger variation in the value of the funds without adjusting tax rules or benefits.