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...

Evaluating risk measures, premiums, and capital allocation based on dependent multi-losses is a notoriously difficult task. In this paper, we demonstrate how this can be successfully accomplished when losses follow the multivariate Pareto distribution of the second kind, which is an attractive...

The risk exposure of a business line could be perceived in many ways and is sensitive to the exercise that is performed. One way is to understand the effect of some common/reference risk over the performance of the business line in question, but irrespective of the modelling exercise, the...

Asymptotic results are obtained for several conditional measures of association. The chosen random variables are the first two order statistics and the total sum within a random sum. Many of the results have confirmed the “one-jump” property of the risk model. Non-trivial limits are obtained...

Various concepts appeared in the existing literature to evaluate the risk exposure of a financial or insurance firm/subsidiary/line of business due to the occurrence of some extreme scenarios. Many of those concepts, such as Marginal Expected Shortfall or Tail Conditional Expectation, are simply...

The classical problem of identifying the optimal reinsurance arrangement for a one-period model is examined under some risk measure criteria. We develop a new methodology via a two-stage optimisation procedure which allows us to not only recover some existing results in the literature, but also...