Multiple losses, Ex Ante moral hazard, and the implications for umbrella policies

Under certain cost conditions the optimal insurance policy offers full coverage above a deductible, as Arrow and others have shown. However, many insurance policies currently provide coverage against several losses although the possibilities for the insured to affect the loss probabilities by several prevention activities (multiple moral hazard) are substantially different. This article shows that optimal contracts under multiple moral hazard generally call for complex reimbursement schedules. It also examines the conditions under which different types of risks can optimally be covered by a single insurance policy and argues that the case for umbrella policies under multiple moral hazard is limited in practice.