Résumé (EN)

Abstract: Insurance policies seldom provide policy holders with complete coverage against losses.Most policies limit coverage with deductibles or include an upper limit. A new explanation for existenceof deductibles and upper limits on coverage is given based on multiplicity of agents' priors and cautiousbehavior. Two models are studied. In the rst, both agents have capacities which are epsilon-contaminations of a given prior with di erent epsilons. It is shown that if the insurer (respectively theinsured) takes more into account maximal losses than the insured (respectively the insurer), then theoptimal contract has an upper limit (respectively includes a deductible). In the second model, agentsare RDEU maximizers. It is proven that if the insurer is very sensitive to the certainty e ect (andtherefore overweights his maximal loss) while the insured is mildly sensitive, then the optimal contracthas an upper limit. If furthermore, the insured disregards events of low probability and neglects hisminimal loss, the optimal contract includes a deductible. We lastly combine and compare the twomodels.