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
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.
Boolean valued analysis, conditional risk measures, duality theory, transfer principle.
PDF file (328 kB)
510.898, 517,98, 519.866
MSC: 03C90, 46H25, 91B30
J. M. Zapata, “A boolean valued analysis approach to conditional risk”, Vladikavkaz. Mat. Zh., 21:4 (2019), 71–89
Citation in format AMSBIB
\paper A boolean valued analysis approach to conditional risk
\jour Vladikavkaz. Mat. Zh.
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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
A. G. Kusraev, S. S. Kutateladze, “Some applications of boolean valued analysis”, J. Appl. Log.-IFCOLOG, 7:4 (2020), 427–457
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