Optimum and risk-class pricing of annuities

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 transfers if insurance firms are unable to precommit their customers. On the other hand, public insurance plans that do not distinguish between 'risk-class' realizations are also inefficient. It is impossible, a-priori, to rank these alternatives from a welfare point of view.