报告时间：6月15日上午10点
报告地点：统计楼103
报告人：Professor Jun Cai, Department of Statistics and Actuarial Science, University of Waterloo, Canada
报告题目：Generalized quantiles based on the rank-dependent expected utility theory
摘要：When the regulator makes a decision on a solvency capital requirement for a risk, the regulator will face both a shortfall risk and an over-required capital risk. We assume that the regulator has different attitudes for the two kinds of risks and measure them based on the rank-dependent expected utility (RDEU) theory. We propose new risk measures, called the generalized quantiles based on the RDEU theory, as the solutions that minimize the total measures of the two types of risks. The generalized quantiles can not only recover distortion risk measures, expectiles, and the risk measures introduced by Bellini et al. (2014), but also produce other interesting risk measures. Moreover, the generalized quantiles reduce to the generalized shortfall risk measures induced from the cumulative prospect theory (CPT), which can be viewed as the extensions of the shortfall risk measures introduced by F\ollmer and Schied (2002). In this paper, we study the properties of the generalized quantiles and provide the consistent non-parametric estimators for them as well. We also discuss the applications of the estimators in backtesting the generalized quantiles. Moreover, we give the sufficient and necessary conditions for the generalized shortfall risk measures to be coherent. In addition, we obtain the dual and Kusuoka representations of the generalized shortfall risk measures. (This talk is based on joint works with Tiantian Mao)