Linear price equilibria in a non-exclusive insurance market

Abstract

We consider a competitive insurance market in which agents can privately enter into multicontractual insurance relationships and undertake hidden actions. We study the existence of linear equilibria when insurance companies do not have any restriction on their pricing rules. We provide conditions under which a linear equilibrium exists. We show that two different types of linear equilibria could exist: A first one in which insurance companies make zero expected profits, and a second one in which they make strictly positive expected profits. We also analyze the welfare properties of the linear equilibria. We show that they are not always second best Pareto optimal.

Hidden Insurance in a Moral Hazard Economy

“…Asset position limits or bid-ask spreads prevent deviations in Bisin and Gottardi (1999), and latent contracts support a competitive high-effort equilibrium in Bisin and Guaitoli's (2004) model with two effort levels (see also Hellwig 1983a,b). Loss and Piaser (2013) extend this analysis allowing for continuous effort, and show that non-concavity of the objective function may let individuals be indifferent between exerting an interior amount of effort (and insuring the loss partially) and setting the effort at the lowest possible level (and overinsuring). In equilibrium, the insurance price is fair for the probabilities implied by the low effort choice, but unfair for the probabilities implied by the higher effort choice.…”