Asset selection based on estimating stress-strength probabilities: The case of returns following three-parameter generalized extreme value distributions
Analyzing the statistical behavior of the assets' returns has shown to be an interesting approach to perform asset selection. In this work, we explore a stress-strength reliability approach to perform asset selection based on probabilities of the type $ P(X < Y) $ when both $ X $ and $ Y...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024116?viewType=HTML |
| _version_ | 1797354572514066432 |
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| author | Felipe S. Quintino Melquisadec Oliveira Pushpa N. Rathie Luan C. S. M. Ozelim Tiago A. da Fonseca |
| author_facet | Felipe S. Quintino Melquisadec Oliveira Pushpa N. Rathie Luan C. S. M. Ozelim Tiago A. da Fonseca |
| author_sort | Felipe S. Quintino |
| collection | DOAJ |
| description | Analyzing the statistical behavior of the assets' returns has shown to be an interesting approach to perform asset selection. In this work, we explore a stress-strength reliability approach to perform asset selection based on probabilities of the type $ P(X < Y) $ when both $ X $ and $ Y $ follow a generalized extreme value (GEV) distribution with three parameters. At first, we derive new analytical and closed form relations in terms of the extreme value $ \mathbb{H} $-function, which have been obtained under fewer parameter restrictions compared to similar results in the literature. To show the performance of our results, we include a Monte-Carlo simulation study and we investigate the application of the reliability measure $ P(X < Y) $ in selecting financial assets with returns characterized by the distributions $ X $ and $ Y $. Therefore, rather than the conventional approach of comparing the expected values of $ X $ and $ Y $ based on modern portfolio theory, we delve into the metric $ P(X < Y) $ as an alternative parameter for assessing better returns. |
| first_indexed | 2024-03-08T13:52:22Z |
| format | Article |
| id | doaj.art-872a9dc7735f4fdea815b472534a726e |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-08T13:52:22Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-872a9dc7735f4fdea815b472534a726e2024-01-16T01:31:52ZengAIMS PressAIMS Mathematics2473-69882024-01-01912345236810.3934/math.2024116Asset selection based on estimating stress-strength probabilities: The case of returns following three-parameter generalized extreme value distributionsFelipe S. Quintino 0Melquisadec Oliveira 1Pushpa N. Rathie 2Luan C. S. M. Ozelim3Tiago A. da Fonseca41. Department of Statistics, University of Brasília, Brasília, DF 70.910-900, Brazil1. Department of Statistics, University of Brasília, Brasília, DF 70.910-900, Brazil1. Department of Statistics, University of Brasília, Brasília, DF 70.910-900, Brazil2. Department of Civil and Environmental Engineering, University of Brasília, Brasília, DF 70.910-900, Brazil3. Gama Engineering College, University of Brasília, Brasília, DF 72.444-240, BrazilAnalyzing the statistical behavior of the assets' returns has shown to be an interesting approach to perform asset selection. In this work, we explore a stress-strength reliability approach to perform asset selection based on probabilities of the type $ P(X < Y) $ when both $ X $ and $ Y $ follow a generalized extreme value (GEV) distribution with three parameters. At first, we derive new analytical and closed form relations in terms of the extreme value $ \mathbb{H} $-function, which have been obtained under fewer parameter restrictions compared to similar results in the literature. To show the performance of our results, we include a Monte-Carlo simulation study and we investigate the application of the reliability measure $ P(X < Y) $ in selecting financial assets with returns characterized by the distributions $ X $ and $ Y $. Therefore, rather than the conventional approach of comparing the expected values of $ X $ and $ Y $ based on modern portfolio theory, we delve into the metric $ P(X < Y) $ as an alternative parameter for assessing better returns.https://www.aimspress.com/article/doi/10.3934/math.2024116?viewType=HTMLstress-strength reliability$ \mathbb{h} $-functionsgeneralized extreme value distribution |
| spellingShingle | Felipe S. Quintino Melquisadec Oliveira Pushpa N. Rathie Luan C. S. M. Ozelim Tiago A. da Fonseca Asset selection based on estimating stress-strength probabilities: The case of returns following three-parameter generalized extreme value distributions AIMS Mathematics stress-strength reliability $ \mathbb{h} $-functions generalized extreme value distribution |
| title | Asset selection based on estimating stress-strength probabilities: The case of returns following three-parameter generalized extreme value distributions |
| title_full | Asset selection based on estimating stress-strength probabilities: The case of returns following three-parameter generalized extreme value distributions |
| title_fullStr | Asset selection based on estimating stress-strength probabilities: The case of returns following three-parameter generalized extreme value distributions |
| title_full_unstemmed | Asset selection based on estimating stress-strength probabilities: The case of returns following three-parameter generalized extreme value distributions |
| title_short | Asset selection based on estimating stress-strength probabilities: The case of returns following three-parameter generalized extreme value distributions |
| title_sort | asset selection based on estimating stress strength probabilities the case of returns following three parameter generalized extreme value distributions |
| topic | stress-strength reliability $ \mathbb{h} $-functions generalized extreme value distribution |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024116?viewType=HTML |
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