In this paper, we provide a stable limit theorem for the asymptotic distribution of the sample average value-at-risk when the distribution of the underlying random variable X describing portfolio returns is heavy-tailed. We illustrate the convergence rate in the limit theorem assuming that X has...

The seminal work of Mandelbrot and Fama, carried out in the sixties, suggested the class of alpha-stable laws as a probabilistic model of financial assets returns. Stable distributions possess several properties which make plausible their application in the field of finance - heavy tails, excess...

The paper introduces a new, moment-based representation of version independent, coherent risk functionals for distributions with a finite second moment. The representation is based on L-moments. We analyze the second- and the third-order approximations and provide a method for constructing...