风险度量:从单变量到矩阵变量的概括

IF 0.3 4区经济学 Q4 BUSINESS, FINANCE

Journal of Risk Pub Date : 2019-07-29 DOI:10.21314/JOR.2021.003

M. A. Arias-Serna, F. Caro-Lopera, Jean-Michel Loubes

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引用次数: 1

摘要

当潜在风险因素在单变量和矩阵变量设置中遵循贝塔分布时，本文开发了一种估计风险价值和条件风险价值的方法。为此，我们将矩阵自变量的高斯超几何函数理论与正定矩阵上的积分联系起来。对于形状参数a和b的某些选择，开发了风险度量的分析表达式。更一般地，给出了β分布损失变量的任何参数化的风险度量的数值解。最后将提出的风险测度用于量化信用风险中潜在的经济损失风险。

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Risk Measures: A Generalization from the Univariate to the Matrix-variate

This paper develops a method for estimating value-at-risk and conditional value-at-risk when the underlying risk factors follow a beta distribution in a univariate and a matrix-variate setting. For this purpose, we connect the theory of the Gaussian hypergeometric function of matrix argument and integration over positive definite matrixes. For certain choices of the shape parameters, a and b, analytical expressions of the risk measures are developed. More generally, a numerical solution for the risk measures for any parameterization of beta-distributed loss variables is presented. The proposed risk measures are finally used for quantifying the potential risk of economic loss in credit risk.

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来源期刊

Journal of Risk BUSINESS, FINANCE-

CiteScore

1.00

自引率

14.30%

发文量

期刊介绍： This international peer-reviewed journal publishes a broad range of original research papers which aim to further develop understanding of financial risk management. As the only publication devoted exclusively to theoretical and empirical studies in financial risk management, The Journal of Risk promotes far-reaching research on the latest innovations in this field, with particular focus on the measurement, management and analysis of financial risk. The Journal of Risk is particularly interested in papers on the following topics: Risk management regulations and their implications, Risk capital allocation and risk budgeting, Efficient evaluation of risk measures under increasingly complex and realistic model assumptions, Impact of risk measurement on portfolio allocation, Theoretical development of alternative risk measures, Hedging (linear and non-linear) under alternative risk measures, Financial market model risk, Estimation of volatility and unanticipated jumps, Capital allocation.