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Shapley Allocation, Diversification and Services in Operational Risk

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Abstract

A method of allocating Operational Risk regulatory capital using the Shapley method for a large number of business units, supported by a service, is proposed. A closed-form formula for Shapley allocations is developed under two principal assumptions. First, if business units form coalitions, the value added to the coalition by a new entrant depends on a constant proportionality factor. This factor represents the diversification that can be achieved by combining operational risk losses. Second, that the service should reduce the capital payable by business units, and that this reduction is calculated as an integral part of the allocation process. We ensure that allocations of capital charges are acceptable to and are understandable by both risk and senior managers. The results derived are applied to recent loss data

Suggested Citation

  • Peter Mitic & Bertrand K. Hassani, 2015. "Shapley Allocation, Diversification and Services in Operational Risk," Documents de travail du Centre d'Economie de la Sorbonne 15056, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:15056
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    Keywords

    Allocation; Shapley; operational risk; diversification; service; Game theory; capital value;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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