Dual representations of quasiconvex compositions with applications to\n systemic risk

2021/08/29 by Ararat, Çağın, M ucahit Ayg un, Aygün, Mücahit +2
Decision Sciences · Economics, Econometrics and Finance · #46A20 #46N10 #52A01 #91G45 #FOS: Economics and business #FOS: Mathematics #Health Systems, Economic Evaluations, Quality of Life #Insurance and Financial Risk Management #Optimization and Control (math.OC) #Risk Management (q-fin.RM) #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.2108.12910

openalex publication_date 2021/08/29 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Motivated by the problem of finding dual representations for quasiconvex\nsystemic risk measures in financial mathematics, we study quasiconvex\ncompositions in an abstract infinite-dimensional setting. We calculate an\nexplicit formula for the penalty function of the composition in terms of the\npenalty functions of the ingredient functions. The proof makes use of a\nnonstandard minimax inequality (rather than equality as in the standard case)\nthat is available in the literature. In the second part of the paper, we apply\nour results in concrete probabilistic settings for systemic risk measures, in\nparticular, in the context of Eisenberg-Noe clearing model. We also provide\nnovel economic interpretations of the dual representations in these settings.\n

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