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Abstract In this review article, we discuss how premium principles arise in theory and in practice. We propose three methods that actuaries use to derive premium principles: (1) thead hoc methodin which the actuary simply proposes a (potentially) reasonable premium principle then studies its properties; (2) thecharacterization methodin which the actuary lists the properties that she wants the premium principle to satisfy, then finds (all) the premium principles that satisfy those properties; and (3) theeconomic methodin which the actuary espouses an economic theory and determines the resulting premium principle. These methods are not exclusive, as we note in the article.
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