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

Listed author(s):
  • Hirbod Assa

    ()

    (Institute for Financial and Actuarial Mathematics, University of Liverpool, Liverpool L69 7ZX, UK)

  • Manuel Morales

    ()

    (Department of Mathematics and Statistics, University of Montreal, CP. 6128 Succ. Centre-Ville, Montreal, QC H3C 3J7, Canada)

  • Hassan Omidi Firouzi

    ()

    (Senior Enterprise Model Risk Analyst, Royal Bank of Canada, 200 Bay St, Toronto, ON M5J 2J1, Canada)

Registered author(s):

    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.

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    Article provided by MDPI, Open Access Journal in its journal Risks.

    Volume (Year): 4 (2016)
    Issue (Month): 3 (August)
    Pages: 1-20

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    Handle: RePEc:gam:jrisks:v:4:y:2016:i:3:p:30-:d:76031
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    10. Jan Dhaene & Andreas Tsanakas & Emiliano A. Valdez & Steven Vanduffel, 2012. "Optimal Capital Allocation Principles," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(1), pages 1-28, March.
    11. Kim, Joseph H.T. & Hardy, Mary R., 2009. "A capital allocation based on a solvency exchange option," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 357-366, June.
    12. Lemaire, Jean, 1984. "An Application of Game Theory: Cost Allocation," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 14(01), pages 61-81, April.
    13. Tsanakas, Andreas, 2004. "Dynamic capital allocation with distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 223-243, October.
    14. Julien Trufin & Hansjoerg Albrecher & Michel M Denuit, 2011. "Properties of a Risk Measure Derived from Ruin Theory," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 36(2), pages 174-188, December.
    15. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted risk capital allocations," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 263-269, October.
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