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.
Citation: 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[J]. AIMS Mathematics, 2024, 9(1): 2345-2368. doi: 10.3934/math.2024116
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.
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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[J]. AIMS Mathematics, 2024, 9(1): 2345-2368. doi: 10.3934/math.2024116
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