Allocation of risk capital in a cost cooperative game induced by a modified expected shortfall

The standard theory of coherent risk measures fails to consider individual institutions as part of a system which might itself experience instability and spread new sources of risk to the market participants. This paper fills this gap and proposes a cooperative market game where agents and institutions play the same role. We take into account a multiple institutions framework where some institutions jointly experience distress, and evaluate their individual and collective impact on the remaining institutions in the market. To carry out the analysis, we define a new risk measure (SCoES) which is a generalization of the Expected Shortfall of and we characterize the riskiness profile as the outcome of a cost cooperative game played by institutions in distress. Each institution’s marginal contribution to the spread of riskiness towards the safe institutions in then evaluated by calculating suitable solution concepts of the game such as the Banzhaf–Coleman and the Shapley–Shubik values.