Optimal intergenerational insurance is examined in a stochastic overlapping generations endowment economy with limited enforcement of risk-sharing transfers. Transfers are chosen by a benevolent planner who maximizes the expected discounted utility of all generations while respecting the participation constraint of each generation. We show that the optimal sustainable intergenerational insurance is history dependent. The risk from a shock is unevenly spread into the future, generating heteroscedasticity and autocorrelation of consumption even in the long run. The optimum can be interpreted as a social security scheme characterized by a minimum welfare entitlement for the old and state-contingent entitlement thresholds.
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