On fairness of systemic risk measures

Francesca Biagini (), Jean-Pierre Fouque (), Marco Frittelli () and Thilo Meyer-Brandis ()
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Francesca Biagini: University of Munich
Jean-Pierre Fouque: University of California
Marco Frittelli: Università degli Studi di Milano
Thilo Meyer-Brandis: University of Munich

Finance and Stochastics, 2020, vol. 24, issue 2, No 8, 513-564

Abstract: Abstract In our previous paper “A unified approach to systemic risk measures via acceptance sets” (Mathematical Finance, 2018), 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 prove a 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 maximisation problem which has the same solution as the minimisation problem associated to the systemic risk measure. In addition, the optimiser in the dual formulation provides a risk allocation which is fair from the point of view of the individual financial institutions. The case with exponential utilities which allows explicit computation is treated in detail.

Keywords: Systemic risk measures; Random allocations; Risk allocation; Fairness; 60A99; 91B30; 91G10; 93D99 (search for similar items in EconPapers)
JEL-codes: C69 G1 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s00780-020-00417-4

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