On one problem of portfolio analysis under soft constraints

A model of a minimal risk portfolio under conditions of hybrid uncertainty of the possibility-probability type based on the principle of expected possibility has been developed and studied. The peculiarity of this model is that the "softness" of the restriction on the level of expected return is modeled by replacing a clear restriction with a possibilistic binary relation. The model example shows how the softness of the constraint affects a set of quasi-effective estimates of an investment portfolio.