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

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Institute for Financial and Actuarial Mathematics, University of Liverpool, Liverpool L69 7ZX, UK
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Department of Mathematics and Statistics, University of Montreal, CP. 6128 Succ. Centre-Ville, Montreal, QC H3C 3J7, Canada
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Senior Enterprise Model Risk Analyst, Royal Bank of Canada, 200 Bay St, Toronto, ON M5J 2J1, Canada
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Author to whom correspondence should be addressed.
Academic Editor: José Garrido
Risks 2016, 4(3), 30; https://doi.org/10.3390/risks4030030
Received: 25 May 2015 / Revised: 6 July 2016 / Accepted: 15 July 2016 / Published: 16 August 2016
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
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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