A Perception-Based Estimation of Uncertainty and its Application to Financial Portfolios

A risk-minimizing portfolio model under uncertainty with randomness and fuzziness is discussed. By a perception-based extension of estimations for fuzzy random variables, the risk-minimizing portfolio problem is developed. In the uncertainty model, the randomness and fuzziness are evaluated respectively by the probabilistic expectation and mean values with evaluation weights and -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 risk-minimizing portfolio problem. It is shown that the solution is a tangency portfolio. A numerical example is given to illustrate our idea. Key–Words: Uncertainty modeling, perception-based estimation, fuzzy random variable, portfolio, riskminimizing, possibility-necessity weight, pessimistic-optimistic index.