Generic Fréchet differentiability of convex operators

Generic G&eaux- Differentiability of Convex Functions on Small Sets

The theory of generic differentiability of convex functions on Banach spaces is by now a well-explored part of infinite-dimensional geometry. All the attempts to solve this kind of problem have in common, as a working hypothesis, one special feature of the finite-dimensional case. Namely, convex functions are always considered to be defined on convex sets with nonempty interior. But typically, ...

Generic Fr6chet -differentiability of Convex Functions on Small Sets

On the Economic Meaning of Machina's Fréchet Differentiability Assumption

This note shows that Machina's (1982) assumption that preferences over lotteries are smooth has some economic implications. We show that Fr echet di erentiability implies that preferences represent second order risk aversion (as well as conditional second order risk aversion). This implies, among other things, that decision makers buy full insurance only at the absence of marginal loading. We a...

Fréchet differentiability in statistical inference for time series

Asymptotic results on distributional behavior of robust estimates in stationary time series models are complex on both technical and assumptional side compare for instance L. Mancini, E. Ronchetti, F. Trojani (2005) and N. Muler, D. Pena, V. J. Yohai (2009). Considering the fact that econometric time series tend to be stationary rather than are stationary and that testing unit root hypotheses i...

Differentiability of convex functions outside small sets

Small sets. We are going to present some results of the following type: under a suitable assumption on a normed space X, each continuous convex function, defined on an open convex set A ⊂ X, is (Gâteaux or Fréchet) differentiable outside a set which is in some sense small. It is natural to ask that a nonempty family S ⊂ 2X whose elements are considered “small sets” satisfy the following conditi...