Optimal Portfolio under Non-Extensive Statistical Mechanics and Value-at-Risk Constraints
Pan Zhaoa, b, Jixia Wangc, Yu Songd
aCollege of Finance and Mathematics, West Anhui University, Lu'an, Anhui, China
bFinancial Risk Intelligent Control and Prevention Institute of West Anhui University, Lu'an, Anhui, China
cSchool of Mathematics and Information Sciences, Henan Normal University, Xinxiang, Henan, China
dSchool of Economics and Management, Nanjing University of Science and Technology, Nanjing, Jiangsu, China
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In this study, we consider the optimal portfolio selection problem with a value-at-risk constraint in the non-extensive statistical mechanics framework. We propose a portfolio selection model, which is suitable not only for normal return distributions, but also for non-normal return distributions. Using Chinese stock data, under the normal and q-Gaussian return distributions, we provide empirical results. The results indicate that portfolio selections under the q-Gaussian return distributions are considerably different from those under the normal return distributions. Moreover, by using the q-Gaussian distribution, the underestimated portfolio risk can be effectively avoided.

topics: Tsallis entropy, q-Gaussian distribution, value-at-risk, optimal portfolio