A Perception-Based Portfolio Under Uncertainty: Minimization of Average Rates of Falling

A perception-based portfolio model under uncertainty is discussed. In the proposed model, randomness and fuzziness are evaluated respectively by the probabilistic expectation and the mean values with evaluation weights and *** -mean functions. The means, the variances and the covariances fuzzy numbers/fuzzy random variables are evaluated in the possibility case and the necessity case, and the rate of return with portfolios is estimated by the both random factors and imprecise factors. In the portfolio model, the average rate of falling is minimized using average value-at-risks as a coherent risk measure. By analytical approach, we derive a solution of the portfolio problem to minimize the average rate of falling. A numerical example is given to illustrate our idea.