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Risks 2013, 1(1), 14-33; doi:10.3390/risks1010014
Article

Evaluating Risk Measures and Capital Allocations Based on Multi-Losses Driven by a Heavy-Tailed Background Risk: The Multivariate Pareto-II Model

1
,
2,*  and 3
1 Cass Business School, City University, London EC1Y 8TZ, UK 2 Faculty of Mathematics and Computer Science, Ovidius University of Constanta, 124 Mamaia Blvd, 900527 Constanta, and Institute of Mathematical Statistics and Applied Mathematics, 13 Septembrie 13, 050711 Bucharest, Romania 3 Department of Statistical and Actuarial Sciences, University of Western Ontario, London, OntarioN6A 5B7, Canada
* Author to whom correspondence should be addressed.
Received: 14 January 2013 / Revised: 31 January 2013 / Accepted: 25 February 2013 / Published: 5 March 2013
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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 that 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 distortion risk measure; weighted premium; weighted allocation; tail value at risk; conditional tail expectation; multivariate Pareto distribution
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Asimit, A.V.; Vernic, R.; Zitikis, R. Evaluating Risk Measures and Capital Allocations Based on Multi-Losses Driven by a Heavy-Tailed Background Risk: The Multivariate Pareto-II Model. Risks 2013, 1, 14-33.

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