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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, Open Access Journal, 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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    1. repec:mnb:finrev:v:16:y:2017:i:3:p:74-97 is not listed on IDEAS

    More about this item

    Keywords

    capital allocation; Euler allocation method; coherent risk measures; Lévy insurance processes; risk measures on the space of stochastic processes;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • G0 - Financial Economics - - General
    • G1 - Financial Economics - - General Financial Markets
    • G2 - Financial Economics - - Financial Institutions and Services
    • G3 - Financial Economics - - Corporate Finance and Governance
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics
    • M4 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting
    • K2 - Law and Economics - - Regulation and Business Law

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