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. In compliance with an approach adopted by Shapley and Shubik (1969), this paper proposes a cooperative market game where agents and institutions play the same role can be developed. We take into account a multiple institutions framework where some of them jointly experience distress events in order to evaluate their individual and collective impact on the remaining institutions in the market. To carry out this analysis, we define a new risk measure (SCoES), generalising the Expected Shortfall of Acerbi (2002) and we characterise the riskiness profile as the outcome of a cost cooperative game played by institutions in distress (a similar approach was adopted by Denault 2001). 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.