Probationary Periods and Time-Dependent Deductibles in Insurance Markets with Adverse Selection

Abstract

Insurance policies sometimes allow the extent of coverage to vary over the life of the policy according to the timing of the loss. In markets with adverse selection, contracts with time-dependent coverage are shown to provide a desirable screening mechanism whenever ex post information about the date of occurrence of a loss is available to insurers. In the situation considered, individuals face the risk of a given monetary loss over some given time horizon; the loss can occur only once and its date of occurrence is random. As in the standard analysis of separating equilibria under adverse selection, high-risk individuals purchase full coverage, while low risks are offered partial coverage; in contrast to the standard analysis, coverage can be made dependent on the date of occurrence of the loss. The paper shows under what conditions coverage for the low risks should be constant, increasing or decreasing over the life of the policy.