## Approaches to Conditional Risk

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2012
##### Authors
Filipović, Damir
Vogelpoth, Nicolas
Journal article
Published
##### Published in
SIAM Journal on Financial Mathematics ; 3 (2012), 1. - pp. 402-432. - eISSN 1945-497X
##### Abstract
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 module-based convex analysis where conditional risk measures are defined on $L^p$-type modules. Both approaches utilize general duality theory for vector-valued 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 module-based 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 module-based convex analysis where conditional risk measures are defined on $L^p$-type modules. Both approaches utilize general duality theory for vector-valued 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 module-based convex analysis is well suited to the concept of conditional risk measures.
510 Mathematics
##### Cite This
ISO 690FILIPOVIĆ, Damir, Michael KUPPER, Nicolas VOGELPOTH, 2012. Approaches to Conditional Risk. In: SIAM Journal on Financial Mathematics. 3(1), pp. 402-432. eISSN 1945-497X. Available under: doi: 10.1137/090773076
BibTex
@article{Filipovic2012-01Appro-40916,
year={2012},
doi={10.1137/090773076},
title={Approaches to Conditional Risk},
number={1},
volume={3},
journal={SIAM Journal on Financial Mathematics},
pages={402--432},
author={Filipović, Damir and Kupper, Michael and Vogelpoth, Nicolas}
}

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