A unified approach to systemic risk measures via acceptance sets. (7th February 2018)

• Record Type: Journal Article
• Authors: Biagini, Francesca; Fouque, Jean‐Pierre; Frittelli, Marco; Meyer‐Brandis, Thilo
• Is Part Of: Mathematical finance. Volume 29:Number 1(2019)
• Page Start: 329
• Page End: 367
• Publication Date: 2018-02-07
• Subjects: acceptance set -- aggregation -- systemic risk -- risk measures; Business mathematics -- Periodicals; 332
• DOI: 10.1111/mafi.12170
• Languages: English
• ISSNs: 0960-1627

Abstract

Abstract: 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.