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...

This contribution relates to the use of risk measures for determining (re)insurers' economic capital requirements. Alternative sets of properties of risk measures are discussed. Furthermore, methods for constructing risk measures via indifference arguments, representation results and...

The Aumann-Shapley (1974) value, originating in cooperative game theory, is used for the allocation of risk capital to portfolios of pooled liabilities, as proposed by Denault (2001). We obtain an explicit formula for the Aumann-Shapley value, when the risk measure is given by a distortion...

The theory and practice of risk measurement provides a point of intersection between risk management, economic theories of choice under risk, financial economics and actuarial pricing theory. This paper provides a review of these interrelationships, from the perspective of an insurance company...

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...