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Risks 2016, 4(3), 30; doi:10.3390/risks4030030

On the Capital Allocation Problem for a New Coherent Risk Measure in Collective Risk Theory

1
Institute for Financial and Actuarial Mathematics, University of Liverpool, Liverpool L69 7ZX, UK
2
Department of Mathematics and Statistics, University of Montreal, CP. 6128 Succ. Centre-Ville, Montreal, QC H3C 3J7, Canada
3
Senior Enterprise Model Risk Analyst, Royal Bank of Canada, 200 Bay St, Toronto, ON M5J 2J1, Canada
*
Author to whom correspondence should be addressed.
Academic Editor: José Garrido
Received: 25 May 2015 / Revised: 6 July 2016 / Accepted: 15 July 2016 / Published: 16 August 2016
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Abstract

In this paper we introduce a new coherent cumulative risk measure on a subclass in the space of càdlàg processes. This new coherent risk measure turns out to be tractable enough within a class of models where the aggregate claims is driven by a spectrally positive Lévy process. We focus our motivation and discussion on the problem of capital allocation. Indeed, this risk measure is well-suited to address the problem of capital allocation in an insurance context. We show that the capital allocation problem for this risk measure has a unique solution determined by the Euler allocation method. Some examples and connections with existing results as well as practical implications are also discussed. View Full-Text
Keywords: capital allocation; Euler allocation method; coherent risk measures; Lévy insurance processes; risk measures on the space of stochastic processes capital allocation; Euler allocation method; coherent risk measures; Lévy insurance processes; risk measures on the space of stochastic processes
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. (CC BY 4.0).

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MDPI and ACS Style

Assa, H.; Morales, M.; Omidi Firouzi, H. On the Capital Allocation Problem for a New Coherent Risk Measure in Collective Risk Theory. Risks 2016, 4, 30.

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