The portfolio problem with present value modelled by a discrete trapezoidal fuzzy number

The main purpose of this article is to present the characteristics of a multi-asset portfolio in the case of its present value estimated by a discrete trapezoidal fuzzy number. The benefits of owning a security are evaluated according to an expected fuzzy discount factor. The ambiguity risk is assessed by an energy measure and indistinctness risk is evaluated by Kosko’s entropy measure. In the paper, the relationship between the expected fuzzy discount factor for a portfolio and the expected fuzzy discount factors for its components is derived. An analogous relationship between the values of the energy measure is presented. Model is illustrated by means of a profound numerical case study.