Ambiguity and insurance: robust capital requirements and premiums

Many insurance and reinsurance contracts are contingent on events such as hurricanes, terrorist attacks or political upheavals whose probabilities are not known with precision. There is a body of experimental evidence showing that higher premiums are charged for these “ambiguous” contracts, which may in turn inhibit (re)insurance transactions, but little research analysing explicitly how and why premiums are loaded in this way. In this paper we model the effect of ambiguity on the capital requirement of a (re)insurer whose objectives are profit maximisation and robustness. The latter objective means that it must hold enough capital to meet a survival constraint across a range of available estimates of the probability of ruin. We provide characterisations of when one book of insurance is more ambiguous than another and formally explore the circumstances in which a more ambiguous book requires at least as large a capital holding. This analysis allows us to derive several explicit formulae for the price of ambiguous insurance contracts, each of which identifies the extra ambiguity load. JEL Classification Numbers: D81, G22.