Optimum and risk-class pricing of annuities

When information on longevity (survival functions) is unknown early in life, individuals have an interest in insuring themselves against moving into different 'risk-classes' as their life expectancy is revealed. The First-Best allocation involves transfers across states of nature. With symmetric information, competitive equilibrium separates different risk classes and cannot provide such transfers because insurance firms are unable to precommit. When utility is invariant to risk-class realisation, the optimum entails uniform consumption and optimum retirement age independent of risk-class and an optimum social security scheme is superior to competitive equilibrium. When preferences depend on risk-class, welfare ranking of systems becomes indeterminate.