We introduce a class of quantile-based risk measures that generalize Value at Risk (VaR) and, likewise Expected Shortfall (ES), take into account both the frequency and the severity of losses. Under VaR a single confidence level is assigned regardless of the size of potential losses. We allow...

Optimal risk transfers are derived within an insurance group consisting of two separate legal entities, operating under potentially different regulatory capital requirements and capital costs. Consistently with regulatory practice, capital requirements for each entity are computed by either a...

A simple formula for non-discriminatory insurance pricing is introduced. This formula is based on the assumption that certain individual (discriminatory) policyholder information is not allowed to be used for insurance pricing. The suggested procedure can be summarized as follows: First, we...