A risk-minimizing model under uncertainty in portfolio

Abstract

A risk-minimizing portfolio model under uncertainty is discussed. In the uncertainty model, the randomness and fuzziness are evaluated respectively by the probabilistic expectation and mean values with evaluation weights and A-mean functions. The means, variances and the measurements of fuzziness for fuzzy numbers/fuzzy random variables are applied in the possibility case and the necessity case, and a risk estimation is derived from both random factors and fuzzy factors in the model. By quadratic programming approach, we derive a solution of the riskminimizing portfolio problem. It is shown that the solution is a tangency portfolio. A numerical example is given to illustrate our idea. © Springer-Verlag Berlin Heidelberg 2007.