We develop a general methodology for deriving probabilistic guarantees solutions of robust optimization problems. Our analysis applies broadly to any convex compact uncertainty set and c...

This paper presents a robust stability and performance analysis for an uncertainty set delivered by classical prediction error identi"cation. This nonstandard uncertainty set, which is a set of parametrized transfer functions with a parameter vector in an ellipsoid, contains the true system at a certain probability level. Our robust stability result is a necessary and su$cient condition for the...

Robust portfolio optimization aims to maximize the worst-case portfolio return given that the asset returns are allowed to vary within a prescribed uncertainty set. If the uncertainty set is not too large, the resulting portfolio performs well under normal market conditions. However, its performance may substantially degrade in the presence of market crashes, that is, if the asset returns mater...

This paper presents a robust stability and performance analysis for an uncertainty set delivered by classical prediction error identi cation. This nonstandard uncertainty set, which is a set of parametrized transfer functions with a parameter vector in an ellipsoid, contains the true system at a certain probability level. Our robust stability result is a necessary and suÆcient condition for the...

In this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. Finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.

We discuss problems for convex Bayesian decision making and uncertainty representation. These include the inability to accommodate various natural and useful constraints and the possibility of an ana­ log of the classical Dutch Book being made against an agent behaving in accordance with convex Baye­ sian prescriptions. A more general set�based Bayesi� anism may be as tractable and would avoid ...