Consistency of Risk Loaded Premiums

The meaning of consistency of increased limit factors (ILF) is reconsidered and a new test of the consistency condition is proposed. It is shown that the three major measures of risk satisfy the new consistency test with no restrictions. The problems of specifying consistent risk-loaded rates for high limits are discussed and a revised subtraction formula is given for the case, where risk is measured by the certainty equivalent of an exponential utility function. Risk "profile" curves are suggested as a method to emphasize the objective aspects of risk load. A new practical meaning is suggested for the old consistency condition. Keywords: Claim Size Modeling, Loss Distribution, Deductibles, Increased Limits, Excess of Loss