Issue: 2018/Vol.28/No.1, Pages 57-74
THE PORTFOLIO PROBLEM WITH PRESENT VALUE MODELLED BY A DISCRETE TRAPEZOIDAL FUZZY NUMBER
Cite as: K. Piasecki, J. Siwek. The portfolio problem with present value modelled by a discrete trapezoidal fuzzy number. Operations Research and Decisions 2018: 28(1), 57-74. DOI 10.5277/ord180104
A multi-asset portfolio in the case of its present value estimated by a discrete trapezoidal fuzzy number has been assessed. The benefits of owning a security have been evaluated according to an expected fuzzy discount factor. The ambiguity risk has been assessed by an energy measure and indistinctness risk has been evaluated by Kosko’s entropy measure. The relationship between the expected fuzzy discount factor for a portfolio and the expected fuzzy discount factors for its components has been derived. An analogous relationship between the values of the energy measure has been presented. The model has been illustrated by means of a profound numerical case study.
Keywords: portfolio, present value, discrete trapezoidal fuzzy number, discount factor
Received: 6 November 2017 Accepted: 9 April 2018