A family of premium principles based on mixtures of TVaRs

Abstract

Risk-adjusted distributions are commonly used in actuarial science to de ne premium principles. In this paper, we claim that an appropriate risk-adjusted distribution, besides of satisfying other desirable properties, should be well-behaved under conditioning with respect to the original risk distribution. Based on a sequence of such risk-adjusted distributions, we introduce a family of premium principles that gradually incorporate the degree of risk-aversion of the insurer in the safety loading. Members of this family are particular distortion premium principles than can be represented as mixtures of TVaRs, where the weights in the mixture re ect the attitude toward risk of the insurer. We make a systematic study of this family of premium principles.