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.