Upper and lower variances under model uncertainty and their applications in finance

Abstract

In this paper, we consider the upper and lower variances under model uncertainty and propose the corresponding algorithm. We then focus on the linear combination of maximally distributed and [Formula: see text]-normally distributed random variables, and obtain the explicit formula to calculate Value-at-Risk (VaR) where the underlying risk is captured by such combination with mean-uncertainty and variance-uncertainty simultaneously. As an application in finance, the general [Formula: see text]-VaR prediction with model uncertainty is also discussed.