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

See all articles by Alexandru Vali Asimit

Alexandru Vali Asimit

Cass Business School, City, University of London

Raluca Vernic

Ovidius University of Constanta

Ricardas Zitikis

University of Western Ontario - Department of Statistical and Actuarial Sciences

Date Written: January 13, 2013

Abstract

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

Asimit, Alexandru Vali and Vernic, Raluca and Zitikis, Ricardas, Evaluating Risk Measures and Capital Allocations Based on Multi-Losses Driven by a Heavy-Tailed Background Risk: The Multivariate Pareto-II Model (January 13, 2013). Risks, 2013, Volume 1, Issue 1, p.14-33. Available at SSRN: https://ssrn.com/abstract=2200174 or http://dx.doi.org/10.2139/ssrn.2200174

Alexandru Vali Asimit (Contact Author)

Cass Business School, City, University of London ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Raluca Vernic

Ovidius University of Constanta ( email )

b-dul Mamaia nr. 124
Constanta, 900527
Romania

Ricardas Zitikis

University of Western Ontario - Department of Statistical and Actuarial Sciences ( email )

1151 Richmond Street
Suite 2
London, Ontario N6A 5B8
Canada

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