Some new classes of consistent risk measures. (English) Zbl 1188.91087

Summary: Many types of insurance premium principles and/or risk measures can be characterized by means of a set of axioms, which in many cases are rather arbitrarily chosen and not always in accordance with economic reality. In the present paper we generalize Yaari’s risk measure by relaxing his axioms. In addition, we derive translation invariant minimal Orlicz risk measures, which we call Haezendonck risk measures, and obtain sufficient conditions on the risk measure of Bernoulli risks to fulfill additivity and superadditivity properties for Orlicz premium principles.


91B30 Risk theory, insurance (MSC2010)
60E05 Probability distributions: general theory
60E15 Inequalities; stochastic orderings
62E10 Characterization and structure theory of statistical distributions
62P05 Applications of statistics to actuarial sciences and financial mathematics
91B82 Statistical methods; economic indices and measures
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