Résumé en anglais

In this paper, we want to characterize the optimal health insurance contract with adverse selection and moral hazard. We assume that policyholders differ by the permanent health status loss and choose an unobservable preventive effort in order to reduce the probability of illness which is ex-ante identical. The difference in illness'after-effect modifies policyholders' preventive actions. By the way, they differ in probabilities of illness leading to a situation close to Rothschild and Stiglitz 'model. In this case, we show that the optimal contract exhibits a deductible for the high health risk type since a higher after effect implies a higher preventive effort and then a lower probability of illness rather than for the low health risk type.