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arXiv · 1711.09833

A Boolean valued analysis approach to conditional risk

José Miguel Zapata
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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 inside of 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.

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José Miguel Zapata. 2017-11-27. A Boolean valued analysis approach to conditional risk. https://arxiv.org/abs/1711.09833

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