A new portfolio selection problem in bubble condition under uncertainty: Application of Z-number theory and fuzzy neural network

摘要

In this paper, a new mathematical formulation for a portfolio selection problem is developed. This model is based on the difference between fundamental value and market value of assets. The proposed model is especially applicable in bubble conditions. Input data of the developed model are subjected to uncertainty. To consider data uncertainty, the Z-number theory is employed. Additionally, a fuzzy neural network is used to predict market value of assets in different economic conditions as input data of the developed model. To show advantages of the proposed model, its results are compared to the mean absolute deviation (MAD), Conditional Value at Risk (CVaR), and Value at Risk (VaR). Results show that the deterministic formulation of proposed model performs better than MAD, CVaR, and VaR in bubble condition. Moreover, fuzzy formulations of all mentioned models perform better than their deterministic formulations in terms of capturing risk of a bubble. Finally, results illustrate that application of the Z-number theory in the proposed model makes the new portfolio selection problem reliable in bubble condition with respect to calculating risk of bubble bursting and proposing the best portfolio among all deterministic and nondeterministic formulations in bubble conditions.