Regulator-Based Risk Statistics for Portfolios

Abstract

<jats:p>Risk statistic is a critical factor not only for risk analysis but also for financial application. However, the traditional risk statistics may fail to describe the characteristics of regulator-based risk. In this paper, we consider the regulator-based risk statistics for portfolios. By further developing the properties related to regulator-based risk statistics, we are able to derive dual representation for such risk.</jats:p>

Regulator-Based Risk Statistics with Scenario Analysis

“…Next, from the statistical point of view by Kou et al [6], the behavior of a random variable can be characterized by its samples. At the same time, one can also incorporate scenario analysis into this framework, see Antolín-Díaz et al [7].…”

“…It has also been extensively studied in the last decade, for example, see Kou et al [6], Ahmed et al [9], Assa and Morales [10], Hassler et al [11], Sun et al [12], Tian and Jiang [13], Tian and Suo [14], and the references therein. However, as pointed out by Deng and Sun [7], people sometimes only pay attention to the losses caused by the risk. us, it is of special sense to derive the risk statistics for such risk, especially the engineering risk.…”

Complex Risk Statistics with Scenario Analysis

“…Later, Tian and Suo [16] obtained dual representations for convex risk statistics, and the corresponding results for quasiconvex risk statistics were obtained by [17]. Deng and Sun [18] focused on the regulator-based risk statistics for portfolios. However, all of these risk statistics are designed to quantify risk of simple component (i.e., a random variable) by its samples.…”