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A unified approach to systemic risk measures via acceptance sets
Author(s) -
Biagini Francesca,
Fouque JeanPierre,
Frittelli Marco,
MeyerBrandis Thilo
Publication year - 2019
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12170
Subject(s) - systemic risk , convexity , monotonic function , cash , risk analysis (engineering) , coherent risk measure , actuarial science , cash flow , computer science , econometrics , economics , risk management , business , expected shortfall , mathematics , finance , financial crisis , macroeconomics , mathematical analysis
We specify a general methodological framework for systemic risk measures via multidimensional acceptance sets and aggregation functions. Existing systemic risk measures can usually be interpreted as the minimal amount of cash needed to secure the system after aggregating individual risks. In contrast, our approach also includes systemic risk measures that can be interpreted as the minimal amount of cash that secures the aggregated system by allocating capital to the single institutions before aggregating the individual risks. An important feature of our approach is the possibility of allocating cash according to the future state of the system (scenario‐dependent allocation). We also provide conditions that ensure monotonicity, convexity, or quasi‐convexity of our systemic risk measures.