Calibrating Distribution Models from PELVE

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-04-19 DOI:10.1080/10920277.2023.2211648

H. Assa, Liyuan Lin, Ruodu Wang

引用次数: 0

Abstract

The Value-at-Risk (VaR) and the Expected Shortfall (ES) are the two most popular risk measures in banking and insurance regulation. To bridge between the two regulatory risk measures, the Probability Equivalent Level of VaR-ES (PELVE) was recently proposed to convert a level of VaR to that of ES. It is straightforward to compute the value of PELVE for a given distribution model. In this paper, we study the converse problem of PELVE calibration, that is, to find a distribution model that yields a given PELVE, which may either be obtained from data or from expert opinion. We discuss separately the cases when one-point, two-point, n-point and curve constraints are given. In the most complicated case of a curve constraint, we convert the calibration problem to that of an advanced differential equation. We apply the model calibration techniques to estimation and simulation for datasets used in insurance. We further study some technical properties of PELVE by offering a few new results on monotonicity and convergence.

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从PELVE校准分布模型

风险价值（VaR）和预期缺口（ES）是银行和保险监管中最受欢迎的两种风险度量。为了在这两种监管风险度量之间架起桥梁，最近提出了风险值ES的概率等效水平（PELVE），以将风险值的水平转换为ES的水平。对于给定的分布模型，计算PELVE的值很简单。在本文中，我们研究了PELVE校准的逆问题，即找到一个产生给定PELVE的分布模型，该分布模型可以从数据中获得，也可以从专家意见中获得。分别讨论了一点约束、两点约束、n点约束和曲线约束的情况。在曲线约束最复杂的情况下，我们将校准问题转换为高级微分方程的校准问题。我们将模型校准技术应用于保险数据集的估计和模拟。通过提供一些关于单调性和收敛性的新结果，我们进一步研究了PELVE的一些技术性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.