An estimation model of value-at-risk portfolio under uncertainty

A value-at-risk 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 λ-mean functions. The means, the variances and the measurements of imprecision for fuzzy numbers/fuzzy random variables are evaluated in the possibility case and the necessity case, and the rate of return in portfolio is estimated regarding the both random factors and imprecise factors. By analytical approach, we derive a solution of the value-at-risk portfolio problem. A numerical example is given to illustrate our idea.