@article{scholars11171,
            note = {cited By 1},
         journal = {IEEJ Transactions on Electrical and Electronic Engineering},
          number = {11},
            year = {2019},
             doi = {10.1002/tee.22986},
           title = {Sensitivity-based fuzzy multi-objective portfolio model with Value-at-Risk},
           pages = {1639--1651},
       publisher = {John Wiley and Sons Inc.},
          volume = {14},
            issn = {19314973},
          author = {Zhang, H. and Watada, J. and Wang, B.},
        keywords = {Electronic trading; Genetic algorithms; Particle swarm optimization (PSO); Reactive power; Sensitivity analysis; Uncertainty analysis; Value engineering, Calculation formula; Degree of stability; fuzzy VaR; Fuzzy variable; Improved particle swarm optimization algorithms; New York Stock Exchange; Portfolio model; Portfolio selection, Financial markets},
        abstract = {To quantitatively discuss the effects and uncertainties of yield changes in each stock for portfolio selection results and then to provide a more reliable portfolio solution for investors, sensitivity analysis is introduced to improve the multi-objective portfolio model with fuzzy VaR (SA-VaR-FMOPSM). Compared with the existing fuzzy VaR multi-objective portfolio model (VaR-FMOPSM), the calculation formulas of expected and VaR value of parabolic fuzzy variable are derived when stock yields are set as a more generalized parabolic fuzzy variable as well as the sensitivity of the total objective to the VaR-FMOPSM model is defined. Meanwhile, based on the fuzzy simulation technique, the model adapted to a series of different distributed fuzzy variable, an improved particle swarm optimization algorithm (IPSO) is used for numerical simulations. To illustrate the proposed model, New York Stock Exchange and National Association of Securities Dealers Automated Quotations-Global Select Market (NASDAQ-GS) stock data were selected for empirical testing, and to better reflect the true value of each stock for each day, we selected the ex-right price data in the experiment, a comparison with the existing fuzzy VaR multi-objective portfolio model (VaR-FMOPSM) is performed. The results show that the fuzzy VaR multi-objective portfolio model based on the sensitivity analysis method can effectively identify and quantitatively analyze the sensitivity of individual stocks to yield changes, i.e. that can identify which stock has more stable yields and that can calculate the degree of stability, then to obtain stable portfolio solutions. In addition, compared with the VaR-FMOPSM model, our sensitivity-based improved model with the IPSO algorithm also performs better than Genetic Algorithm and Simulate Anneal Algorithm (SA), it provides the same performance on this point. {\^A}{\copyright} 2019 Institute of Electrical Engineers of Japan. Published by John Wiley \& Sons, Inc. {\^A}{\copyright} 2019 Institute of Electrical Engineers of Japan. Published by John Wiley \& Sons, Inc.},
             url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85074183061&doi=10.1002\%2ftee.22986&partnerID=40&md5=6ade6285d9b68876e950fc1a46fef4e6}
}