Exact and approximate expressions for the reliability of stable Lévy random variables with applications to stock market modelling

For almost a century, stable Lévy random variables have been considered as statistical models to stock market data. Due to the difficulty associated with the evaluation of their probability distribution function, practical applications have been limited to the existence of accurate computational routines. In the present paper, the exact expression for the reliability of two stable Lévy random variables is analytically obtained in terms of the H-function. An approximate expression, in terms of simpler functions, is also derived in order to make the application of the results easier. Computational codes are provided to aid the evaluation of the formulas derived. Finally, the applicability of the new expressions is illustrated by modelling stock return data.