On July 2 from 10:30 to 13:00 - Room 207, at LUISS, viale Romania 32, Roma, prof. Cagin Ararat from Bilkent University will give two talks:
Talk I
Title: Set-valued quasiconvex risk measures
Abstract: Set-valued risk measures are defined naturally in environments where it is necessary to measure the risk of a random vector. In this talk, we consider set-valued risk measures that are defined as compositions of two set-valued functions. This class of risk measures is rich enough to cover many examples of the systemic risk measures studied in the recent literature. We pay special attention to the properties of the constituent set-valued functions that guarantee the quasiconvexity of the composite risk measure. It turns out that the so-called natural quasiconvexity property, an old but not so well-known property between convexity and quasiconvexity, plays a key role in the study of these risk measures. The main results provide dual representations for quasiconvex, naturally quasiconvex and convex compositions in terms of the dual functions of the constituents.
Talk II
Title: Computation of systemic risk measures
Abstract: Various approaches to measure systemic risk have been proposed in the recent literature using multivariate functionals. These functionals are typically defined in terms of a so-called aggregation function, which takes into account the interconnectedness of the institutions in the network, and a univariate risk measure applied to the random output of the aggregation function. In this talk, we specialize into the Eisenberg-Noe and Rogers-Veraart network models and formulate the corresponding systemic risk measures as large-scale vector optimization problems. While the former model yields a convex problem which can be solved efficiently using non-smooth optimization techniques, the efficient frontier for the latter model turns out to be the boundary of a non-convex set.