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Euler allocations in the presence of non-linear reinsurance: comment on Major (2018)

Pesenti, S. M., Millossovich, P. ORCID: 0000-0001-8269-7507 and Tsanakas, A. ORCID: 0000-0003-4552-5532 (2018). Euler allocations in the presence of non-linear reinsurance: comment on Major (2018). Insurance: Mathematics and Economics, doi: 10.1016/j.insmatheco.2018.09.001

Abstract

Major (2018) discusses Euler/Aumann-Shapley allocations for non-linear positively homogeneous portfolios. For such portfolio structures, plausibly arising in the context of reinsurance, he defines a distortion-type risk measure that facilitates assessment of ceded and net losses with reference to gross portfolio outcomes. Subsequently, Major (2018) derives explicit formulas for Euler allocations for this risk measure, thus (sub-)allocating ceded losses to the portfolio’s original components. In this comment, we build on Major’s (2018) insights but take a somewhat different direction, to consider Euler capital allocations for distortion risk measures directly
applied to homogeneous portfolios. Explicit formulas are derived and our approach is compared with that of Major (2018) via a numerical example.

Publication Type: Article
Additional Information: © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords: Distortion risk measures, Capital allocation, Euler allocation, Aumann-Shapley, Reinsurance Aggregation
Subjects: H Social Sciences > HD Industries. Land use. Labor > HD61 Risk Management
Q Science > QA Mathematics
Departments: Cass Business School > Actuarial Science & Insurance
URI: http://openaccess.city.ac.uk/id/eprint/20437
[img] Text - Accepted Version
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