This paper investigates equilibrium in an insurance market where risk classification is restricted. Insurance demand is characterised by an iso-elastic function with a single elasticity parameter. We characterise the equilibrium by three quantities: equilibrium premium; level of adverse selection (in the economist's sense); and `loss coverage', defined as the expected population losses compensated by insurance. We consider both equal elasticities for high and low risk-groups, and then different elasticities. In the equal elasticities case, adverse selection is always higher under pooling than under risk-differentiated premiums, while loss coverage first increases and then decreases with demand elasticity. We argue that loss coverage represents the efficacy of insurance for the whole population; and therefore that if demand elasticity is sufficiently low, adverse selection is not always a bad thing.
Hao, M., Macdonald, A. S., Tapadar, P., & Thomas, R. G. (2016). Insurance Loss Coverage Under Restricted Risk Classification: The Case of Iso-elastic Demand. ASTIN Bulletin: The Journal of the IAA, 46(2), 265-291. https://doi.org/10.1017/asb.2016.6