In response to the unprecedented uncertain rare events of the last decade, we derive an optimal portfolio choice problem in a semi-closed form by integrating price diffusion ambiguity, volatility diffusion ambiguity, and jump ambiguity occurring in the traditional stock market and the...

In this paper, we study the general notions of upper and lower variances, which were initially introduced by Peter Walley for the bounded random variables. The properties of upper and lower variances and new formulas for calculation of them are provided. We take US markets for case study, which...