Ambiguity and insurance: robust capital requirements and premiums
Many insurance and reinsurance contracts are contingent on events such ashurricanes, terrorist attacks or political upheavals whose probabilities are not known with precision. There is a body of experimental evidence showing thathigher premiums are charged for these ï¿½ambiguousï¿½ contracts, which may in turn inhibit (re)insurance transactions, but little research analysing explicitlyhow 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 musthold enough capital to meet a survival constraint across a range of availableestimates of the probability of ruin. We provide characterisations of when onebook of insurance is more ambiguous than another and formally explore thecircumstances in which a more ambiguous book requires at least as large acapital holding. This analysis allows us to derive several explicit formulae forthe price of ambiguous insurance contracts, each of which identifies the extraambiguity load.
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