A risk-minimizing portfolio model with fuzziness

A variance-minimizing portfolio model is discussed under randomness and fuzziness. The randomness and fuzziness are evaluated respectively by the probabilistic expectation and mean values with evaluation weights and lambda-mean functions. The means and variances for fuzzy numbers/fuzzy random variables are applied in the possibility case and the necessity case. By quadratic programming approach, we derive a solution of the risk-minimizing portfolio problem and we show the solution is a tangency portfolio. A numerical example is given to illustrate our idea.