In this paper, we investigate the asymptotic behavior of the portfolio diversification ratio based on Value-at-Risk (quantile) under dependence uncertainty, which we refer to as "worst-case diversification limit." We show that the worst-case diversification limit is equal to the upper limit of...

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...

Tsanakas and Barnett (2002) employed concepts from cooperative game theory (Aumann and Shapley, 1974) for the allocation of risk capital to portfolios of pooled liabilities, when distortion risk measures (Wang et al., 1997) are used. In this paper we generalise previously obtained results in...

We discuss classes of risk measures in terms both of their axiomatic definitions and of the economic theories of choice that they can be derived from. More specifically, expected utility theory gives rise to the exponential premium principle, proposed by Gerber (1974), Dhaene et al. (2003),...

We use mean-variance hedging in discrete time, in order to value a terminal insurance liability. The prediction of the liability is decomposed into claims development results, that is, yearly deteriorations in its conditional expected value. We assume the existence of a tradeable derivative with...