Abstract We formulate a superhedging theorem in the presence of transaction costs and model uncertainty. Asset prices are assumed continuous uncertainty is modeled parametric setting. Our proof relies on new topological framework which no Krein–Smulian type available.

A generalization of the classical Leray-Schauder fixed point theorem, based on the infinitedimensional Borsuk-Ulam type antipode construction, is proposed. Two completely different proofs based on the projection operator approach and on a weak version of the well known Krein-Milman theorem are presented. MIRAMARE – TRIESTE May 2007 [email protected]; [email protected]

We study the recently introduced Krein structure (indefinite metric) of the N = 1 supersymmetry and present the way into physical applications outside path integral methods. From the mathematical point of view some perspectives are mentioned at the end of the paper.

Krein space operator-theoretic methods are used to prove that the operator (sgn x) d is similar to a selfadjoint operator in the Hilbert space L2 (R) . Let L be a symmetric ordinary differential expression. Spectral properties of the operators associated with the weighted eigenvalue problem Lu = )wu have been studied extensively. When w is positive, this problem leads to a selfadjoint problem i...