Ambiguity and insurance: capital requirements and premiums

Many insurance contracts are contingent on events such as hurricanes, terrorist attacks or political upheavals, whose probabilities are ambiguous. This paper offers a theory to underpin the large body of empirical evidence showing that higher premiums are charged under ambiguity. We model a (re)insurer who maximises profit subject to a survival constraint that is sensitive to the range of estimates of the probability of ruin, as well as the insurer’s attitude towards this ambiguity. We characterise when one book of insurance is more ambiguous than another and general circumstances in which a more ambiguous book requires at least as large a capital holding. We subsequently derive several explicit formulae for the price of insurance contracts under ambiguity, each of which identifies the extra ambiguity load.