Aggregation of Randomly Weighted Large Risks

IMA Journal of Management Mathematics, 28(3), pp. 403–419. doi:10.1093/imaman/dpv020.

21 Pages Posted: 29 Jan 2012 Last revised: 8 Feb 2018

See all articles by Alexandru Vali Asimit

Alexandru Vali Asimit

Cass Business School, City, University of London

Enkelejd Hashorva

University of Lausanne, Actuarial Department

Dominik Kortschak

University of Lausanne

Date Written: February 13, 2015

Abstract

Asymptotic tail probabilities for linear combinations of randomly weighted order statistics are approximated under various assumptions. One key assumption is the asymptotic independence for all risks. Therefore, it is not surprising that the maxima represents the most influential factor when one investigates the tail behaviour of our considered risk aggregation, which for example, can be found in the reinsurance market. This extreme behaviour confirms the "one big jump" property that has been vastly discussed in the existing literature in various forms whenever the asymptotic independence is present. An illustration of our results together with a specific application are explored under the assumption that the underlying risks follow the multivariate Log-normal distribution.

Keywords: Davis-Resnick tail property; Extreme value distribution; Max-domain of attraction; Mitra-Resnick model; Risk aggregation

Suggested Citation

Asimit, Alexandru Vali and Hashorva, Enkelejd and Kortschak, Dominik, Aggregation of Randomly Weighted Large Risks (February 13, 2015). IMA Journal of Management Mathematics, 28(3), pp. 403–419. doi:10.1093/imaman/dpv020.. Available at SSRN: https://ssrn.com/abstract=1993114 or http://dx.doi.org/10.2139/ssrn.1993114

Alexandru Vali Asimit (Contact Author)

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

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Enkelejd Hashorva

University of Lausanne, Actuarial Department ( email )

Unil Dorigny, Batiment Internef
Lausanne, 1015
Switzerland

Dominik Kortschak

University of Lausanne ( email )

Lausanne, Vaud CH-1015
Switzerland

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