When information on longevity (survival functions) is unknown early in life, individuals have an interest to insure themselves against future "risk-class" classification. Accordingly, the First-Best typically involves transfers across states of nature. Competitive equilibrium cannot provide such...

In a perfectly competitive market for annuities with full information, the price of annuities is equal to individuals (discounted) survival probabilities. That is, prices are actuarially fair. In contrast, the pricing implicit in social security systems invariably allows for cross subsidization...

This paper uses stochastic simulations on calibrated models to assess the optimal degree of reliance on fun ded pensions and on a particular type of unfunded (PAYG) pension. Surprisingly little is known about the optimal split between funded and unfunded systems when there are sources of...