A Boolean valued analysis approach to conditional risk

A Boolean valued analysis approach to conditional risk

Автор: Zapata Jose Miguel

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 4 т.21, 2019 года.

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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.

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Boolean valued analysis, conditional risk measures, duality theory, transfer principle

Короткий адрес: https://sciup.org/143168816

IDR: 143168816   |   DOI: 10.23671/VNC.2019.21.44629

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