A Boolean valued analysis approach to conditional risk
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.
Cite
@article{arxiv.1711.09833,
title = {A Boolean valued analysis approach to conditional risk},
author = {José Miguel Zapata},
journal= {arXiv preprint arXiv:1711.09833},
year = {2019}
}