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

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  • Assa Hirbod
  • Morales Manuel
  • Omidi Firouzi Hassan

Abstract

In this paper we introduce a new coherent cumulative risk measure on $\mathcal{R}_L^p$, the space of c\`adl\`ag processes having Laplace transform. 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 L\'evy process. Moreover, we study the problem of capital allocation in an insurance context and we show that the capital allocation problem for this risk measure has a unique solution determined by the Euler allocation method. Some examples are provided.

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  • Assa Hirbod & Morales Manuel & Omidi Firouzi Hassan, 2013. "On the Capital Allocation Problem for a New Coherent Risk Measure in Collective Risk Theory," Papers 1311.0354, arXiv.org.
    • Handle: RePEc:arx:papers:1311.0354
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    References listed on IDEAS

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    1. Michael Kalkbrener, 2009. "An axiomatic characterization of capital allocations of coherent risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 9(8), pages 961-965.
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    3. Dickson,David C. M., 2010. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521176750.
    4. Louis J. Billera & David C. Heath, 1982. "Allocation of Shared Costs: A Set of Axioms Yielding A Unique Procedure," Mathematics of Operations Research, INFORMS, vol. 7(1), pages 32-39, February.
    5. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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