Capital Allocations for classical and set-valued risk measures

Tsanakas (2009) defined and studied a Capital Allocation Rule (C.A.R.) for Gâteaux-differentiable risk measures inspired to the game theoretic concept of Aumann and Shapley value. His analysis leaves anyway open the case of... [ view full abstract ]

Tsanakas (2009) defined and studied a Capital Allocation Rule (C.A.R.) for Gâteaux-differentiable risk measures inspired to the game theoretic concept of Aumann and Shapley value. His analysis leaves anyway open the case of non Gateaux differentiable risk measures as well as of quasi-convex ones.

We propose and study a family of C.A.R. (for real-valued risk measures) based on their dual representations and on subdifferentials, reducing to Tsanakas' one under Gateaux-differentiability. We also discuss the suitability of the use of quasi-convex risk measures for capital allocation purposes.

We then define and extend capital allocations to set-valued risk measures.