... Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan Shandong250014, China2School of Mathematical Sciences, Qufu Normal University, Qufu Shandong 273165, China3School ... ofEconomics, Shandong University, Jinan Shandong 250014, ChinaAuthors’ contributionsAll authors contributed equally to the manuscript and read and approved the final manuscript.Competing interestsWe ... (11026108,11071141) and XW was supported by the Shandong Province planning Foundation of Social Science (09BJGJ14),Shandong Province Natural Science Foundation (Z200 7A0 4).Author details1School of Mathematic...