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 $Y$ 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.