题目：Nonparametric Inference for Distortion Risk Measures on Tail Regions
Xing Wang is an Assistant Professor in the Department of Mathematics at Illinois State University. She received her Ph.D. in Risk Management and Insurance in J. Mack Robinson College of Business from Georgia State University. She received M.S. in Statistics from Georgia Institute of Technology in 2014, and a B.S. in Mathematics from Tsinghua University in 2013. Her doctoral studied were supported by the prestigious James C. Hickman Scholarship from the Society of Actuaries. Her research interests include risk measures, mortality, annuities and their statistical inference. Her research work focuses on statistical inference about risk measures under the heavy-tailed losses and the valuation processes for the large portfolios of the variable annuities.
Suppose X is some interesting loss and Y is a benchmark variable. Given some extreme scenarios of Y, it is indispensable to measure the tail risk of X by applying a class of univariate risk measure to study the co-movement of the two variables. In this talk, we consider the extreme and nonparametric inference for the distortion risk measures on the tail regions when the extreme scenarios of some benchmark variable are considered. We derive the limit of the proposed risk measures based on Extreme Value Theory. The asymptotics of the risk measures shows the decomposition of the marginal extreme index and the extreme dependence structure which implies how these two pieces of information have influences on the limit of the risk measures. Finally, for practical purpose, we develop a nonparametric estimation method for the distortion risk measures on tail regions and its asymptotic normality is derived.