College of Liberal Arts and Sciences

# Department of Mathematics

## Actuarial Science Seminar

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Title: Upper Bounds for Strictly Concave Distortion Risk Measures on Moment Spaces
Speaker: Steven Vanduffel (Vrije Universiteit Brussel)
Time: Monday, November 12, 2018 at 11:00 am
Place: MONT 214Abstract: The study of worst-case scenarios for risk measures (e.g., Value-at-Risk) when the underlying risk (or portfolio of risks) is not completely specified is a central topic in the literature on robust risk measurement. In this paper, we tackle the open problem of deriving upper bounds for strictly concave distortion risk measures on moment spaces. Building on early results of Rustagi (1957,1976), we show that in general this problem can be reduced to a parametric optimization problem. We completely specify the sharp upper bound (and corresponding maximizing distribution function) when the first moment and any other higher moment are fixed. Specifically, in the case of a fixed mean and variance, we generalize the Cantelli bound for (Tail) Value-at-Risk in that we express the sharp upper bound for a strictly concave distorted expectation as a weighted sum of the mean and standard deviation. This is a joint work with Dries Cornilly (VUB) and Luger Ruschendorf (University of Freiburg).

Organizer: Guojun Gan and Bin Zou