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DOI: 10.23671/VNC.2019.21.44629

A Boolean Valued Analysis Approach to Conditional Risk

Zapata, J. M.
Vladikavkaz Mathematical Journal 2019. Vol. 21. Issue 4.
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.
Keywords: Boolean valued analysis, conditional risk measures, duality theory, transfer principle.
Language: English Download the full text  
For citation: Zapata, J. M. A Boolean Valued Analysis Approach to Conditional Risk, Vladikavkaz Math. J., 2019, vol. 21, no. 4, pp. 71-89. DOI 10.23671/VNC.2019.21.44629
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