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This manuscript has been retracted as it was submitted for publication by Yunquan Song without the knowledge and approval of the co-author Lu Lin.

Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 398750, 10 pages
Research Article

Sublinear Expectation Nonlinear Regression for the Financial Risk Measurement and Management

1School of Mathematics, Shandong University, Jinan 250100, China
2College of Science, China University of Petroleum, Qingdao 266580, China

Received 24 March 2013; Accepted 30 May 2013

Academic Editor: Ivan Ivanov

Copyright © 2013 Yunquan Song and Lu Lin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Financial risk is objective in modern financial activity. Management and measurement of the financial risks have become key abilities for financial institutions in competition and also make the major content in finance engineering and modern financial theories. It is important and necessary to model and forecast financial risk. We know that nonlinear expectation, including sublinear expectation as its special case, is a new and original framework of probability theory and has potential applications in some scientific fields, specially in finance risk measure and management. Under the nonlinear expectation framework, however, the related statistical models and statistical inferences have not yet been well established. In this paper, a sublinear expectation nonlinear regression is defined, and its identifiability is obtained. Several parameter estimations and model predictions are suggested, and the asymptotic normality of the estimation and the mini-max property of the prediction are obtained. Finally, simulation study and real data analysis are carried out to illustrate the new model and methods. In this paper, the notions and methodological developments are nonclassical and original, and the proposed modeling and inference methods establish the foundations for nonlinear expectation statistics.