Evaluating Risk Measures and Capital Allocations Based on Multi-Losses Driven by a Heavy-Tailed Background Risk: The Multivariate Pareto-II Model
Risks, 2013, Volume 1, Issue 1, p.14-33
23 Pages Posted: 13 Jan 2013 Last revised: 17 Nov 2014
Date Written: January 13, 2013
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 model for multi-losses whose dependence and tail heaviness are influenced by a heavy-tailed background risk. A particular attention is given to the distortion and weighted risk measures and allocations, as well as their special cases such as the conditional layer expectation, tail value at risk, and the truncated tail value at risk. We derive formulas which are either of closed form or follow well-defined recursive procedures. In either case, their computational use is straightforward.
Keywords: distortion risk measure, weighted premium, weighted allocation, tail value at risk, conditional tail expectation, multivariate Pareto distribution
JEL Classification: C14, G22
Suggested Citation: Suggested Citation