A boolean valued analysis approach to conditional risk
Vladikavkazskij matematičeskij žurnal, Tome 21 (2019) no. 4, pp. 71-89
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By means of the techniques of Boolean valued analysis, we provide a transfer principle between duality theory of classical convex risk measures and duality theory of conditional risk measures. Namely, a conditional risk measure can be interpreted as a classical convex risk measure within a suitable set-theoretic model. As a consequence, many properties of a conditional risk measure can be interpreted as basic properties of convex risk measures. This amounts to a method to interpret a theorem of dual representation of convex risk measures as a new theorem of dual representation of conditional risk measures. As an instance of application, we establish a general robust representation theorem for conditional risk measures and study different particular cases of it.
@article{VMJ_2019_21_4_a6,
author = {J. M. Zapata},
title = {A boolean valued analysis approach to conditional risk},
journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
pages = {71--89},
publisher = {mathdoc},
volume = {21},
number = {4},
year = {2019},
language = {en},
url = {http://geodesic.mathdoc.fr/item/VMJ_2019_21_4_a6/}
}
J. M. Zapata. A boolean valued analysis approach to conditional risk. Vladikavkazskij matematičeskij žurnal, Tome 21 (2019) no. 4, pp. 71-89. http://geodesic.mathdoc.fr/item/VMJ_2019_21_4_a6/