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A Generalization of the Aumann-Shapley Value for Risk Capital Allocation Problems

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  • Boonen, T.J.

    (Tilburg University, Center For Economic Research)

  • De Waegenaere, A.M.B.

    (Tilburg University, Center For Economic Research)

  • Norde, H.W.

    (Tilburg University, Center For Economic Research)

Abstract

The paper proposes a new method to allocate risk capital to divisions or lines of business within a firm. Existing literature advocates an allocation rule that, in game-theoretic terms, is equivalent to using the Aumann–Shapley value as allocation mechanism. The Aumann–Shapley value, however, is only well-defined if a specific differentiability condition is satisfied. The rule that we propose is characterized as the limit of an average of path-based allocation rules with grid size converging to zero. The corresponding allocation rule is equal to the Aumann–Shapley value if it exists. If the Aumann–Shapley value does not exist, the allocation rule is equal to the weighted average of the Aumann–Shapley values of “nearby” capital allocation problems.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Boonen, T.J. & De Waegenaere, A.M.B. & Norde, H.W., 2012. "A Generalization of the Aumann-Shapley Value for Risk Capital Allocation Problems," Discussion Paper 2012-091, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:2c502ef8-76f0-47f5-ab45-1833b5f41103
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    References listed on IDEAS

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    3. Bergantiños, Gustavo & Groba, Carlos & Sartal, Antonio, 2023. "Applying the Shapley value to the tuna fishery," European Journal of Operational Research, Elsevier, vol. 309(1), pages 306-318.
    4. Takaaki Koike & Marius Hofert, 2020. "Modality for Scenario Analysis and Maximum Likelihood Allocation," Papers 2005.02950, arXiv.org, revised Nov 2020.
    5. Wang, Wei & Xu, Huifu & Ma, Tiejun, 2023. "Optimal scenario-dependent multivariate shortfall risk measure and its application in risk capital allocation," European Journal of Operational Research, Elsevier, vol. 306(1), pages 322-347.
    6. Grechuk, Bogdan, 2023. "Extended gradient of convex function and capital allocation," European Journal of Operational Research, Elsevier, vol. 305(1), pages 429-437.
    7. Gómez, Fabio & Tang, Qihe & Tong, Zhiwei, 2022. "The gradient allocation principle based on the higher moment risk measure," Journal of Banking & Finance, Elsevier, vol. 143(C).
    8. Dóra Balog & Tamás László Bátyi & Péter Csóka & Miklós Pintér, 2014. "Properties of risk capital allocation methods: Core Compatibility, Equal Treatment Property and Strong Monotonicity," CERS-IE WORKING PAPERS 1417, Institute of Economics, Centre for Economic and Regional Studies.
    9. Patrick S. Hagan & Andrew Lesniewski & Georgios E. Skoufis & Diana E. Woodward, 2021. "Portfolio risk allocation through Shapley value," Papers 2103.05453, arXiv.org.

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    More about this item

    Keywords

    capital allocation; risk capital; Aumann-Shapley value; non-differentiability; fuzzy games;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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