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

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  • 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)

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.

Suggested Citation

  • Hirbod Assa & Manuel Morales & Hassan Omidi Firouzi, 2016. "On the Capital Allocation Problem for a New Coherent Risk Measure in Collective Risk Theory," Risks, MDPI, vol. 4(3), pages 1-20, August.
    • Handle: RePEc:gam:jrisks:v:4:y:2016:i:3:p:30-:d:76031
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    References listed on IDEAS

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    Cited by:

    1. Matthias Fischer & Thorsten Moser & Marius Pfeuffer, 2018. "A Discussion on Recent Risk Measures with Application to Credit Risk: Calculating Risk Contributions and Identifying Risk Concentrations," Risks, MDPI, vol. 6(4), pages 1-28, December.
    2. Dóra Balog, 2017. "Capital Allocation in the Insurance Sector," Financial and Economic Review, Magyar Nemzeti Bank (Central Bank of Hungary), vol. 16(3), pages 74-97.
    3. Jaunė, Eglė & Šiaulys, Jonas, 2022. "Asymptotic risk decomposition for regularly varying distributions with tail dependence," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    4. Guusje Delsing & Michel Mandjes & Peter Spreij & Erik Winands, 2021. "On Capital Allocation for a Risk Measure Derived from Ruin Theory," Papers 2103.16264, arXiv.org.

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