The self-insurance clauses puzzle : risk versus ambiguity.

Summary In many insurance contracts, self-insurance clauses appeared. Our objective is to analyze if these self-insurance clauses are justified, function of the observability or not of the self-insurance by the insurer. For this purpose, we propose a theoretical model under risk and ambiguity jointly analysing insurance and self-insurance. Theoretical results show that self-insurance clauses are never justified under risk, and not justified under ambiguity when the self-insurance is observable by the insurer. Moreover, under ambiguity, when the self-insurance is unobservable by the insurer, we show that optimal self-insurance depends on ambiguity preferences. Our results also indicate that insurance and self-insurance are substitutes under risk and under ambiguity only when the self-insurance is observable by the insurer. Under ambiguity, when the self-insurance activity is unobservable, insurance and self-insurance may be or not substitutes when the decision maker has ambiguity aversion.