Uncertain Random Portfolio Optimization Based on Skew Chance Distribution.

The financial market is a complex system owing to its inherent dynamics and indeterminacy. It is well known that uncertainty and randomness are two types of indeterminacy. When there are sufficient historical data, random variables are considered, and when the data are lacking, uncertain variables are considered. In numerous complex systems, such as financial markets, uncertainty and randomness often appear simultaneously. To model the indeterminacy associ-ated with complex systems, including uncertainty and randomness, uncertain random variables are used. Massive shifts in financial market prices can cause considerable discrepancies in the normality assumption of security returns. To overcome the restriction imposed by the normality assumption and capture the non-normality of security returns, this study proposes the concept of skew chance distribution based on a skew-normal uncertainty distribution. A mean-entropy model is presented as an application for portfolio optimization problems. Moreover, a genetic algorithm is implemented in MATLAB to obtain the numerical results.