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This paper studies the normative problem of redistribution between agents who can influence their survival probability through private health spending, but who differ in their attitude towards the risks involved in the lotteries of life to be chosen. For that purpose, a two-period model is developed, where agents' preferences on lotteries of life can be represented by a mean and variance utility function allowing, unlike the expected utility form, some sensitivity to what Allais (Econometrica 21(4), 503-546, 1953) calls the 'dispersion of psychological values'. It is shown that if agents ignore the impact of health spending on the return of their savings, the decentralization of the first-best utilitarian optimum requires intergroup lump sum transfers and group-specific positive taxes on health spending. Under asymmetric information, a differentiated taxation across agents is still required, but subsidizing health spending may be optimal as a way to solve the incentive problem

Optimal tax policy and expected longevity: a mean and variance utility approach