Investigation of the minimum risk portfolio under conditions of hybrid uncertainty based on the weakest $t$-norm

A model of a minimum risk portfolio under conditions of a hybrid uncertainty of a possibilistic-probabilistic type was developed and investigated. The peculiarity of the model is that interaction of fuzzy parameters in it is described by the weakest triangular norm ($t$-norm). A formula for the portfolio variance is obtained, which allows to estimate its risk. The model of feasible portfolios is based on the principle of expected possibility. Its application leads to the removal of possibilistic uncertainty by imposing requirements on the possibility / necessity of meeting the investor's requirements for an acceptable level of portfolio return. An equivalent crisp analog of the model is constructed and demonstrated on a numerical example. Obtained results allow us to build generalized models of portfolio optimization problems with prime objective on processing a hybrid (combined) type of uncertainty.