Guaranteed Renewability with Group Insurance

This paper investigates a multiple-period level premium insurance policy equilibrium in a model in which loss probabilities increase for a fixed time period for a set of persons buying insurance in a group. We show that a level-premium sequence which induces risk averse persons to become and remain members of the group exists. We also show that the availability of the Medicare program can prevent the emergence of optimal level-premium private group insurance, but that a system of bonuses for remaining in the group can permit optimality to be retained.