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Type of Publication:  Journal article 
Publication status:  Published 
Author:  Filipović, Damir; Kupper, Michael; Vogelpoth, Nicolas 
Year of publication:  2012 
Published in:  SIAM Journal on Financial Mathematics ; 3 (2012), 1.  pp. 402432.  eISSN 1945497X 
DOI (citable link):  https://dx.doi.org/10.1137/090773076 
Summary: 
We present and compare two different approaches to conditional risk measures. One approach draws from convex analysis in vector spaces and presents risk measures as functions on $L^p$ spaces, while the other approach utilizes modulebased convex analysis where conditional risk measures are defined on $L^p$type modules. Both approaches utilize general duality theory for vectorvalued convex functions, in contrast to the current literature, in which we find ad hoc dual representations. By presenting several applications such as monotone and (sub)cash invariant hulls with corresponding examples we illustrate that modulebased convex analysis is well suited to the concept of conditional risk measures. Read More: http://epubs.siam.org/doi/abs/10.1137/090773076We present and compare two different approaches to conditional risk measures. One approach draws from convex analysis in vector spaces and presents risk measures as functions on $L^p$ spaces, while the other approach utilizes modulebased convex analysis where conditional risk measures are defined on $L^p$type modules. Both approaches utilize general duality theory for vectorvalued convex functions, in contrast to the current literature, in which we find ad hoc dual representations. By presenting several applications such as monotone and (sub)cash invariant hulls with corresponding examples we illustrate that modulebased convex analysis is well suited to the concept of conditional risk measures.

Subject (DDC):  510 Mathematics 
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FILIPOVIĆ, Damir, Michael KUPPER, Nicolas VOGELPOTH, 2012. Approaches to Conditional Risk. In: SIAM Journal on Financial Mathematics. 3(1), pp. 402432. eISSN 1945497X. Available under: doi: 10.1137/090773076
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