In this paper, we provide an axiomatic approach to general premium principles giving rise to a decomposition into risk , as a generalization of the expected value, and deviation , as a generalization of the variance. We show that, for every premium principle, there exists a maximal risk measure capturing all risky components covered by the insurance prices. In a second step, we consider dual representations of convex risk measures consistent with the premium principle. In particular, we show that the convex conjugate of the aforementioned maximal risk measure coincides with the convex conjugate of the premium principle on the set of all finitely additive probability measures. In a last step, we consider insurance prices in the presence of a not neccesarily frictionless market , where insurance claims are traded. In this setup, we discuss premium principles that are consistent with hedging using securization products that are traded in the market .
We provide an axiomatic approach to general premium principles in a probability-free setting that allows for Knightian uncertainty. Every premium principle is the sum of a risk measure , as a generalization of the expected value, and a deviation measure , as a generalization of the variance. One can uniquely identify a maximal risk measure and a minimal deviation measure in such decompositions. We show how previous axiomatizations of premium principles can be embedded into our more general framework. We discuss dual representations of convex premium principles, and study the consistency of premium principles with a financial market in which insurance contracts are traded .
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In this paper, we
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giving rise to a decomposition into risk
in a probability-free setting that allows for Knightian uncertainty. Every premium principle is the sum of a risk measure
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deviation
a deviation measure
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We show that, for every premium principle, there exists
One can uniquely identify
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capturing all risky components covered by the insurance prices. In a second step, we consider
and a minimal deviation measure in such decompositions. We show how previous axiomatizations of premium principles can be embedded into our more general framework. We discuss
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risk measures consistent with the premium principle. In particular, we show that the convex conjugate of the aforementioned maximal risk measure coincides with the convex conjugate of the premium principle on the set of all finitely additive probability measures. In a last step, we consider insurance prices in the presence of a not neccesarily frictionless market , where insurance claims are traded. In this setup, we discuss premium principles that are consistent with hedging using securization products that are traded in the market
premium principles, and study the consistency of premium principles with a financial market in which insurance contracts are traded