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�…

This paper analyzes risk capital allocation problems. For risk capital allocation problems, the
aim is to allocate the risk capital of a firm to its divisions. Risk capital allocation is of central
importance in risk-based performance measurement. We consider a case in which the
aggregate risk capital is determined via a coherent risk measure. The academic literature
advocates an allocation rule that, in game-theoretic terms, is equivalent to using the Aumann-
Shapley value as solution concept. This value is however not well-defined in case a�…