Papers, ranked by score

Ordered by a blend of empirical rigor (60%) and math complexity (40%).

An analysis of multivariate measures of skewness and kurtosis of skew-elliptical distributions

This paper examines eight measures of skewness and Mardia measure of kurtosis for skew-elliptical distributions. Multivariate measures of skewness considered include Mardia, Malkovich-Afifi, Isogai, Song, Balakrishnan-Brito-Quiroz, M$\acute{o}$ri, Rohatgi and Sz$\acute{e}$kely, Kollo and Srivastava

Holy Grail Math 8.5 Rigor 6 ·  November 30, 2023

Multivariate range Value-at-Risk and covariance risk measures for elliptical and log-elliptical distributions

In this paper, we propose the multivariate range Value-at-Risk (MRVaR) and the multivariate range covariance (MRCov) as two risk measures and explore their desirable properties in risk management. In particular, we explain that such range-based risk measures are appropriate for risk management of re

Holy Grail Math 8.5 Rigor 5.5 ·  May 16, 2023

Analyzing distortion riskmetrics and weighted entropy for unimodal and symmetric distributions under partial information constraints

In this paper, we develop the lower and upper bounds of worst-case distortion riskmetrics and weighted entropy for unimodal, and symmetric unimodal distributions when mean and variance information are available. We also consider the sharp upper bounds of distortion riskmetrics and weighted entropy f

Lab Rats Math 8.5 Rigor 2 ·  April 28, 2025

Worst-cases of distortion riskmetrics and weighted entropy with partial information

In this paper, we discuss the worst-case of distortion riskmetrics for general distributions when only partial information (mean and variance) is known. This result is applicable to general class of distortion risk measures and variability measures. Furthermore, we also consider worst-case of weight

Lab Rats Math 8 Rigor 2 ·  May 29, 2024

Extremal cases of distortion risk measures with partial information

This paper investigates the impact of distributional uncertainty on key risk measures under the partial knowledge of underlying distributions characterized by their first two moments and shape information (specifically symmetry and/or unimodality). We first employ probability inequalities to establi

Lab Rats Math 8 Rigor 2 ·  April 21, 2024

Best- and worst-case Scenarios for GlueVaR distortion risk measure with Incomplete information

This paper derives the best- and worst-case GlueVaR distortion risk measure within a unified framework, based on partial information of the underlying distributions and shape information such as symmetry. In addition, we characterize the extremal distributions of GlueVaR with convex envelopes of the

Lab Rats Math 8 Rigor 1.5 ·  September 30, 2024

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