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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. 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.
    3. 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.
    4. Jaunė, Eglė & Šiaulys, Jonas, 2022. "Asymptotic risk decomposition for regularly varying distributions with tail dependence," Applied Mathematics and Computation, Elsevier, vol. 427(C).

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