Stylized Model of Lévy Process in Risk Estimation
Risk management is a popular and important problem in academia and industry. From a small-scale system, such as city logistics, to a large-scale system, such as the supply chain of a global industrial or financial system, efficient risk management is required to prevent loss from uncertainty. In thi...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/6/1414 |
| _version_ | 1827748907294130176 |
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| author | Xin Yun Yanyi Ye Hao Liu Yi Li Kin-Keung Lai |
| author_facet | Xin Yun Yanyi Ye Hao Liu Yi Li Kin-Keung Lai |
| author_sort | Xin Yun |
| collection | DOAJ |
| description | Risk management is a popular and important problem in academia and industry. From a small-scale system, such as city logistics, to a large-scale system, such as the supply chain of a global industrial or financial system, efficient risk management is required to prevent loss from uncertainty. In this paper, we assume that risk factors follow the Lévy process, and propose a stylized model, based on regression, that can estimate the risk of a complicated system under the framework of nest simulation. Specifically, portfolio risk estimation using the Lévy process is discussed as an example. The stylized model simplifies the risk factors artificially, and provides useful basis functions to fit the portfolio loss with little computational effort. Numerical experiments showed the good performance of the stylized model in estimating risk for the Variance Gamma process and the Normal Inverse Gaussian process, which are two examples of the Lévy process. |
| first_indexed | 2024-03-11T06:13:32Z |
| format | Article |
| id | doaj.art-9b2eb256a87e435fa40c1fe9a3a5319b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T06:13:32Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-9b2eb256a87e435fa40c1fe9a3a5319b2023-11-17T12:28:15ZengMDPI AGMathematics2227-73902023-03-01116141410.3390/math11061414Stylized Model of Lévy Process in Risk EstimationXin Yun0Yanyi Ye1Hao Liu2Yi Li3Kin-Keung Lai4Silc Business School, Shanghai University, Shanghai 200444, ChinaSchool of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, ChinaFundamental Technology Center, China Construction Bank Financial Technology Co., Ltd., Shanghai 200120, ChinaSchool of Management, Xi’an Jiaotong University, Xi’an 710049, ChinaInternational Business School, Shaanxi Normal University, Xi’an 710062, ChinaRisk management is a popular and important problem in academia and industry. From a small-scale system, such as city logistics, to a large-scale system, such as the supply chain of a global industrial or financial system, efficient risk management is required to prevent loss from uncertainty. In this paper, we assume that risk factors follow the Lévy process, and propose a stylized model, based on regression, that can estimate the risk of a complicated system under the framework of nest simulation. Specifically, portfolio risk estimation using the Lévy process is discussed as an example. The stylized model simplifies the risk factors artificially, and provides useful basis functions to fit the portfolio loss with little computational effort. Numerical experiments showed the good performance of the stylized model in estimating risk for the Variance Gamma process and the Normal Inverse Gaussian process, which are two examples of the Lévy process.https://www.mdpi.com/2227-7390/11/6/1414risk estimationstylized modelLévy processnested simulationregression |
| spellingShingle | Xin Yun Yanyi Ye Hao Liu Yi Li Kin-Keung Lai Stylized Model of Lévy Process in Risk Estimation Mathematics risk estimation stylized model Lévy process nested simulation regression |
| title | Stylized Model of Lévy Process in Risk Estimation |
| title_full | Stylized Model of Lévy Process in Risk Estimation |
| title_fullStr | Stylized Model of Lévy Process in Risk Estimation |
| title_full_unstemmed | Stylized Model of Lévy Process in Risk Estimation |
| title_short | Stylized Model of Lévy Process in Risk Estimation |
| title_sort | stylized model of levy process in risk estimation |
| topic | risk estimation stylized model Lévy process nested simulation regression |
| url | https://www.mdpi.com/2227-7390/11/6/1414 |
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