A generalization of the Aumann-Shapley value for risk capital allocation problems

T.J. Boonen*, Anja M.B. Waegenaere, Henk Norde

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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.
Original languageEnglish
Pages (from-to)277-287
JournalEuropean Journal of Operational Research
Volume282
Issue number1
DOIs
Publication statusPublished - Apr 2020

Fingerprint

Shapley Value
Industry
Weighted Average
Differentiability
Generalization
Capital allocation
Risk capital
Shapley value
Allocation problem
Well-defined
Division
Game
Allocation rules
Grid
Path
Line
Zero
Term

Keywords

  • risk management
  • capital allocation
  • risk measure
  • Aumann-Shapley value
  • non-differentiability

Cite this

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title = "A generalization of the Aumann-Shapley value for risk capital allocation problems",
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.",
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A generalization of the Aumann-Shapley value for risk capital allocation problems. / Boonen, T.J.; Waegenaere, Anja M.B.; Norde, Henk.

In: European Journal of Operational Research, Vol. 282, No. 1, 04.2020, p. 277-287.

Research output: Contribution to journalArticleScientificpeer-review

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AB - 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.

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KW - risk measure

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