Upper and lower variances under model uncertainty and their applications in finance

Shan Li, Xinpeng Li and George Xianzhi Yuan
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Shan Li: Research Center for Mathematics and Interdisciplinary Sciences, Frontiers Science Center for Nonlinear Expectations (Ministry of Education), Shandong University, 266237 Qingdao, P. R. China2School of Mathematics, Shandong University, 250100 Jinan, P. R. China
Xinpeng Li: Research Center for Mathematics and Interdisciplinary Sciences, Frontiers Science Center for Nonlinear Expectations (Ministry of Education), Shandong University, 266237 Qingdao, P. R. China2School of Mathematics, Shandong University, 250100 Jinan, P. R. China
George Xianzhi Yuan: School of Business, Sun Yat-sen University, 510275 Guangzhou, P. R. China4College of Science, Chongqing University of Technology, 400054 Chongqing, P. R. China

International Journal of Financial Engineering (IJFE), 2022, vol. 09, issue 01, 1-19

Abstract: In this paper, we consider the upper and lower variances under model uncertainty and propose the corresponding algorithm. We then focus on the linear combination of maximally distributed and G-normally distributed random variables, and obtain the explicit formula to calculate Value-at-Risk (VaR) where the underlying risk is captured by such combination with mean-uncertainty and variance-uncertainty simultaneously. As an application in finance, the general G-VaR prediction with model uncertainty is also discussed.

Keywords: Maximal distribution; mean-uncertainty; G-normal distribution; G-VaR; sublinear expectation; upper and lower variances (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S2424786322500074

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