Risk measures and insurance premium principles

Risk measures based on distorted probabilities have been recently developed in actuarial science and applied to insurance rate making. We propose a ri sk measure that has the properties of risk aversion and diversification, is additive for losses and consistent in its treatment of insurance and inves tment risks. We show that the risk measure based on distorted probabilities is not consistent in its ordering of insurance and investment risks. (C) 2 001 Elsevier Science B.V. All rights reserved.