A Model of Underwriting and Post-Loss Test Without Commitment in Competitive Insurance Market

Abstract

In this article, we establish a model of competitive insurance markets based on Rothschild and Stiglitz (1976) where insurers can perform risk classification tests either before insurance contracts are issued (underwriting) or when coverage claims are filed (post-loss test). However, insurers cannot pre-commit to performing either test in the insurance application period since the tests are costly type-verifications. We derive the perfect Bayesian equilibrium of four cases: no test is used; only one kind of the two types of test is performed; and both tests are performed. The space of parameters where the equilibrium exists in Rothschild and Stiglitz (1976) and Picard (2009) models is extended in our model. The key tradeoff determining which test is utilized lies in the relative magnitude of testing costs. Furthermore, we characterize the contracts provided in the market. Different from the overinsurance counterpart in Picard (2009), the contract for low-risk type with only underwriting test may be either overinsurance, full insurance, or underinsurance in our model.