Consider a portfolio of n identically distributed risks with dependence structure modeled by an Archimedean survival copula. Wüthrich (2003) and Alink et al. (2004) proved that the probability of a large aggregate loss scales like the probability of a large individual loss, times a...

We extend the characterization of the left-monotone risk aversion developed by Ryan (2006) to the case of unbounded random variables. The notion of weak convergence is insufficient for such an extension. It requires the solution of a host of delicate convergence problems. To this end, some...

The Haezendonck–Goovaerts risk measure is based on the premium calculation principle induced by an Orlicz norm, which is defined via an increasing and convex Young function and a parameter q∈(0,1) representing the confidence level. In this paper, we first reestablish the first-order...

The quantification of diversification benefits due to risk aggregation has received more attention in the recent literature. In this paper, we establish second-order expansions of the risk concentration based on the risk measure of conditional tail expectation for a portfolio of n independent...

It is well known that if a random vector with given marginal distributions is comonotonic, it has the largest sum in the sense of the convex order. Cheung (2008) proved that the converse of this assertion is also true, provided that all marginal distribution functions are continuous and that the...

This paper studies capital allocation problems with the aggregate risk exceeding a certain threshold. We propose a novel capital allocation rule based on the Tail Mean–Variance principle. General formulas for the optimal capital allocations are proposed. Explicit formulas for optimal capital...

Let X denote the loss initially assumed by an insurer. In a reinsurance design, the insurer cedes part of its loss, say f(X), to a reinsurer, and thus the insurer retains a loss If(X)=X-f(X). In return, the insurer is obligated to compensate the reinsurer for undertaking the risk by paying the...