Dr. Marco Frittelli (University of Milano, visiting UCSB)

Title: Two applications of quasi-convex analysis

Abstract: We introduce a class of law invariant quasi-convex risk measures based on an appropriate family of acceptance sets. As a particular case, we propose a generalization of the classical notion of the V@R, that takes into account not only the probability of the losses, but the balance between such probability and the amount of the loss. Our second application concerns the evaluation of the quality of the scientific research. We introduc a family of performance measures, called Scientific Research Measures (SRM) that are based on the whole distribution of citations. These SRM are: flexible to fit peculiarities of different areas and seniorities; inclusive, as they comprehend several popular indices;coherent, as they share the same structural properties; calibrated to the particular scientific community.