This paper uses stochastic simulations on calibrated models to assess the steady state impact of different pension arrangements in an environment where financial markets are less than perfect. Surprisingly little is known about the optimal split between funded and unfunded systems when there are sources of uninsurable risk that are allocated in different ways by different types of pension system and where there are imperfections in financial markets (eg transactions costs or adverse selection) . This paper calculates the expected welfare of agents in different economies where in the steady state the importance of unfunded, state pensions differs. We estimate how the optimal level of unfunded, state pensions depends on rate of return and income risks and also upon the actuarial fairness of annuity contracts. We focus on the case of Japan where aging is rapid and unfunded pensions are currently generous.