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Vladikavkaz. Mat. Zh., 2019, Volume 21, Number 4, Pages 71–89 (Mi vmj708)  

This article is cited in 2 scientific papers (total in 2 papers)

A boolean valued analysis approach to conditional risk

J. M. Zapata

University of Konstanz, 10 Universitaetsstrasse, Konstanz D-78457, Germany

Abstract: 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.

Key words: Boolean valued analysis, conditional risk measures, duality theory, transfer principle.

Funding Agency Grant Number
Ministerio de Economía y Competitividad de España MTM2014-57838-C2-1-P
Fundación Séneca 20903/PD/18
The author was partially supported by the grants MINECO MTM2014-57838-C2-1-P and Fundación Séneca 20903/PD/18.


DOI: https://doi.org/10.23671/VNC.2019.21.44629

Full text: PDF file (328 kB)
References: PDF file   HTML file

UDC: 510.898, 517,98, 519.866
MSC: 03C90, 46H25, 91B30
Received: 05.06.2019
Language:

Citation: J. M. Zapata, “A boolean valued analysis approach to conditional risk”, Vladikavkaz. Mat. Zh., 21:4 (2019), 71–89

Citation in format AMSBIB
\Bibitem{Zap19}
\by J.~M.~Zapata
\paper A boolean valued analysis approach to conditional risk
\jour Vladikavkaz. Mat. Zh.
\yr 2019
\vol 21
\issue 4
\pages 71--89
\mathnet{http://mi.mathnet.ru/vmj708}
\crossref{https://doi.org/10.23671/VNC.2019.21.44629}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Aviles Lopez, J. M. Zapata Garcia, “Boolean valued representation of random sets and markov kernels with application to large deviations”, Mathematics, 8:10 (2020), 1848  crossref  isi  scopus
    2. A. G. Kusraev, S. S. Kutateladze, “Some applications of boolean valued analysis”, J. Appl. Log.-IFCOLOG, 7:4 (2020), 427–457  mathscinet  isi
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