Author:
Biagini Francesca,Fouque Jean-Pierre,Frittelli Marco,Meyer-Brandis Thilo
Abstract
AbstractIn 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.
Publisher
Springer Science and Business Media LLC
Subject
Statistics, Probability and Uncertainty,Finance,Statistics and Probability
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