In our previous paper  "A Unified Approach to Systemic Risk Measures via Acceptance Set"  , we have introduced a general class of systemic risk measures that allow  random allocations to individual banks before aggregation of their risks. In the present paper, we address the question of fairness of these allocations and propose a fair allocation of the total risk to individual banks. We show that the dual formulation of the minimization problem identifying the systemic risk measure provides a valuation of the random allocations, which is fair both from the point of view of the society/regulator and from the individual financial institutions. The case with exponential utilities which allows for explicit computation is treated in details.
In our previous paper , "A Unified Approach to Systemic Risk Measures via Acceptance Set" (Mathematical Finance, 2018) , we have introduced a general class of systemic risk measures that allow for random allocations to individual banks before aggregation of their risks. In the present paper, we prove the dual representation of a particular subclass of such systemic risk measures and the existence and uniqueness of the optimal allocation related to them. We also introduce an associated utility maximization problem which has the same optimal solution as the systemic risk measure . In addition, the optimizer in the dual formulation provides arisk allocation which is fair from the point of view of the individual financial institutions. The case with exponential utilities which allows for explicit computation is treated in details.
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address the question of fairness of these allocations and propose a fair allocation of the total risk to individual banks. We show that the dual formulation of the minimization problem identifying the
prove the dual representation of a particular subclass of such systemic risk measures and the existence and uniqueness of the optimal allocation related to them. We also introduce an associated utility maximization problem which has the same optimal solution as the
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