Reinsurance is a versatile risk management strategy commonly employed by insurers to optimize their risk profile. In this paper, we study an optimal reinsurance design problem minimizing a general law-invariant coherent risk measure of the net risk exposure of a generic insurer, in conjunction...

In this article, we study two broad classes of convex order related optimal insurance decision problems, in which the objective function or the premium valuation is a general functional of the expectation, Value-at-Risk and Average Value-at-Risk of the loss variables. These two classes of...

In this paper, we extend the concept of mutual exclusivity proposed by Dhaene and Denuit (1999) to its tail counterpart and baptise this new dependency structure as tail mutual exclusivity. Probability levels are first specified for each component of the random vector. Under this dependency...

It is well known that if a random vector with given marginal distributions is comonotonic, it has the largest sum with respect to the convex order. In this paper, we prove that the converse is also true, provided that each marginal distribution is continuous.

In this paper, we study stochastic orders of scalar products of random vectors. Based on the study of Ma [Ma, C., 2000. Convex orders for linear combinations of random variables. J. Statist. Plann. Inference 84, 11-25], we first obtain more general conditions under which linear combinations of...