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Measuring risk with multiple eligible assets

Content Provider	Springer Nature Link
Author	Farkas, Walter Koch Medina, Pablo Munari, Cosimo
Copyright Year	2014
Abstract	The risk of financial positions is measured by the minimum amount of capital to raise and invest in eligible portfolios of traded assets in order to meet a prescribed acceptability constraint. We investigate nondegeneracy, finiteness and continuity properties of these risk measures with respect to multiple eligible assets. Our finiteness and continuity results highlight the interplay between the acceptance set and the class of eligible portfolios. We present a simple, alternative approach to the dual representation of convex risk measures by directly applying to the acceptance set the external characterization of closed, convex sets. We prove that risk measures are nondegenerate if and only if the pricing functional admits a positive extension which is a supporting functional for the underlying acceptance set, and provide a characterization of when such extensions exist. Finally, we discuss applications to set-valued risk measures, superhedging with shortfall risk, and optimal risk sharing.
Starting Page	3
Ending Page	27
Page Count	25
File Format	PDF
ISSN	18629679
Journal	Mathematics and Financial Economics
Volume Number	9
Issue Number	1
e-ISSN	18629660
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2014-06-30
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Risk measures Multiple eligible assets Acceptance sets Dual representations Set-valued risk measures Risk theory, insurance Ordered topological linear spaces, vector lattices Duality theory Theorems of Hahn-Banach type; extension and lifting of functionals and operators Quantitative Finance Finance/Investment/Banking Financial Economics Game Theory/Mathematical Methods Applications of Mathematics Statistics for Business/Economics/Mathematical Finance/Insurance
Content Type	Text
Resource Type	Article
Subject	Finance Statistics and Probability Statistics, Probability and Uncertainty

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