Semi-static trading strategies make frequent appearances in mathematical finance, where dynamic trading in a liquid asset is combined with static buy-and-hold positions in options on that asset. We show that the space of outcomes of such strategies can have very poor closure properties when all European options for a fixed date T are available for static trading. This causes problems for optima...

We present a Borsuk’s theorem published first in [3] (compare also [4, pages 119–120]). It is slightly generalized, the assumption of metrizability is omitted. We introduce concepts needed for the formulation and the proof of theorems on upper semi-continuous decompositions, retracts, strong deformation retract. However, only those facts that are necessary in the proof have been proved.

We prove that any locally bounded from below, upper semicontinuous v-convex function in any Carnot group is h-convex. §

We introduce a new model for building conditional generative models in a semisupervised setting to conditionally generate data given attributes by adapting the GAN framework. The proposed semi-supervised GAN (SS-GAN) model uses a pair of stacked discriminators to learn the marginal distribution of the data, and the conditional distribution of the attributes given the data respectively. In the s...

We introduce semicontinuity concepts for functions f with values in the space C(Y ) of closed convex subsets of a finite dimensional normed vector space Y by appropriate notions of upper and lower limits. We characterize the upper semicontinuity of f : X → C(Y ) by the upper semicontinuity of the scalarizations σf( · )(y∗) : X → R by the support function. Furthermore, we compare our semicontinu...

Preference: Oral presentation

The irrigation problem is the problem of nding an e cient way to transport a measure μ onto a measure μ−. By e cient, we mean that a structure that achieves the transport (which, following [3], we call tra c plan) is better if it carries the mass in a grouped way rather than in a separate way. This is formalized by considering costs functionals that favorize this property. The aim of this paper...

We consider the problem of representing a (possibly) incomplete preference relation by means of a vector-valued utility function. Continuous and semicontinuous representation results are reported in the case of preference relations that are, in a sense, not “too incomplete.” These results generalize some of the classical utility representation theorems of the theory of individual choice, and pa...