Asymptotic capital allocation based on the higher moment risk measure

IF 0.8 Q4 BUSINESS, FINANCE European Actuarial Journal Pub Date : 2024-03-21 DOI:10.1007/s13385-024-00378-4

Yiqing Chen, Jiajun Liu

引用次数: 0

Abstract

We investigate capital allocation based on the higher moment risk measure at a confidence level \(q\in (0,1)\). To reflect the excessive prudence of today’s regulatory frameworks in banking and insurance, we consider the extreme case with \(q\uparrow 1\) and study the asymptotic behavior of capital allocation for heavy-tailed and asymptotically independent/dependent risks. Some explicit asymptotic formulas are derived, demonstrating that the capital allocated to a specific line is asymptotically proportional to the Value at Risk of the corresponding individual risk. In addition, some numerical studies are conducted to examine their accuracy.

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基于高时刻风险度量的渐近资本分配

我们研究了基于置信水平（q\in (0,1)\）的高矩风险度量的资本分配。为了反映当今银行业和保险业监管框架的过度谨慎，我们考虑了 \(q\uparrow 1\) 的极端情况，并研究了重尾风险和渐近独立/依赖风险的资本分配渐近行为。推导出了一些明确的渐近公式，证明分配给特定项目的资本与相应单个风险的风险值渐近成正比。此外，还进行了一些数值研究，以检验其准确性。

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来源期刊

European Actuarial Journal BUSINESS, FINANCE-

CiteScore

2.30

自引率

8.30%

发文量

期刊介绍： Actuarial science and actuarial finance deal with the study, modeling and managing of insurance and related financial risks for which stochastic models and statistical methods are available. Topics include classical actuarial mathematics such as life and non-life insurance, pension funds, reinsurance, and also more recent areas of interest such as risk management, asset-and-liability management, solvency, catastrophe modeling, systematic changes in risk parameters, longevity, etc. EAJ is designed for the promotion and development of actuarial science and actuarial finance. For this, we publish original actuarial research papers, either theoretical or applied, with innovative applications, as well as case studies on the evaluation and implementation of new mathematical methods in insurance and actuarial finance. We also welcome survey papers on topics of recent interest in the field. EAJ is the successor of six national actuarial journals, and particularly focuses on links between actuarial theory and practice. In order to serve as a platform for this exchange, we also welcome discussions (typically from practitioners, with a length of 1-3 pages) on published papers that highlight the application aspects of the discussed paper. Such discussions can also suggest modifications of the studied problem which are of particular interest to actuarial practice. Thus, they can serve as motivation for further studies.Finally, EAJ now also publishes ‘Letters’, which are short papers (up to 5 pages) that have academic and/or practical relevance and consist of e.g. an interesting idea, insight, clarification or observation of a cross-connection that deserves publication, but is shorter than a usual research article. A detailed description or proposition of a new relevant research question, short but curious mathematical results that deserve the attention of the actuarial community as well as novel applications of mathematical and actuarial concepts are equally welcome. Letter submissions will be reviewed within 6 weeks, so that they provide an opportunity to get good and pertinent ideas published quickly, while the same refereeing standards as for other submissions apply. Both academics and practitioners are encouraged to contribute to this new format. Authors are invited to submit their papers online via http://euaj.edmgr.com.