Dual representations of quasiconvex compositions with applications to systemic risk

Simple item page
buir.advisorArarat, Çağın
dc.contributor.authorAygün, Mücahit
dc.date.accessioned2021-08-17T10:30:59Z
dc.date.available2021-08-17T10:30:59Z
dc.date.copyright2021-07
dc.date.issued2021-07
dc.date.submitted2021-08-09
dc.departmentDepartment of Industrial Engineeringen_US
dc.descriptionCataloged from PDF version of article.en_US
dc.descriptionThesis (Master's): Bilkent University, Department of Industrial Engineering, İhsan Doğramacı Bilkent University, 2021.en_US
dc.descriptionIncludes bibliographical references (leaves 76-78).en_US
dc.description.abstractThe importance of measuring risk in an interconnected financial system has been appreciated recently, due in part to the global financial crisis. In the literature, systemic risk measures are generally represented by the composition of a univariate risk measure and an aggrega-tion function, a function that encodes the structure of the financial network. Having dual representations for systemic risk measures is helpful in providing economic interpretations and offering duality-based computational methods. For a univariate risk measure, a key assumption is that diversification should not increase risk. The mathematical translation of this assumption was considered as convexity earlier in the history of risk measures. Recently, quasiconvexity has been considered as a more accurate translation of diversification. For a single quasiconvex risk measure, dual representations are available in the literature based on the so-called penalty functions. The use of a quasiconvex risk measure in composition with a concave aggregation function results in a quasiconvex systemic risk measure, a multivariate functional on a space of random vectors. Motivated by the problem of finding dual representations for quasiconvex systemic risk measures, we study quasiconvex compositions in an abstract infinite-dimensional setting. We calculate an explicit formula for the penalty function of the composition in terms of the penalty functions of the ingredient functions. The proof makes use of a nonstandard minimax inequality (rather than equality as in the standard case) that is available in the literature. In the last part of the thesis, we apply our results in concrete probabilistic settings for systemic risk measures, in particular, in the context of the Eisenberg-Noe clearing model. We also provide novel economic interpretations of the dual representations in these settings.en_US
dc.description.degreeM.S.en_US
dc.description.statementofresponsibilityby Mücahit Aygünen_US
dc.format.extentvii, 78 leaves ; 30 cm.en_US
dc.identifier.itemidB138375
dc.identifier.urihttp://hdl.handle.net/11693/76445
dc.language.isoEnglishen_US
dc.publisherBilkent Universityen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectQuasiconvex functionen_US
dc.subjectComposition of functionsen_US
dc.subjectMinimax inequalityen_US
dc.subjectRisk measureen_US
dc.subjectSystemic risken_US
dc.subjectDual representationen_US
dc.subjectPenalty functionen_US
dc.titleDual representations of quasiconvex compositions with applications to systemic risken_US
dc.title.alternativeYarıdışbükey bileşkelerin çifteş temsilleri ve sistemik risk üzerine uygulamalarıen_US
dc.typeThesisen_US

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
10411962.pdf
Size:
706.41 KB
Format:
Adobe Portable Document Format
Description:
Full printable version
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.69 KB
Format:
Item-specific license agreed upon to submission
Description:
Download

Collections

Dept. of Industrial Engineering - Master's degree