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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 516291, 6 pages
http://dx.doi.org/10.1155/2014/516291
Research Article

An Upper Bound of Large Deviations for Capacities

School of Mathematics, Shandong University, Jinan 250000, China

Received 23 April 2014; Accepted 22 May 2014; Published 15 June 2014

Academic Editor: Xuejun Xie

Copyright © 2014 Xiaomin Cao. 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.

Linked References

  1. A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, Springer, New York, NY, USA, 2nd edition, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  2. S. Peng, “G-Expectation, G-Brownian motion and related stochastic calculus of Itô’s type,” in Proceedings of the 2005 Abel Symposium, vol. 2, pp. 541–567, Springer, 2006.
  3. P. Artzner, F. Delbaen, J.-M. Eber, and D. Heath, “Coherent measures of risk,” Mathematical Finance, vol. 9, no. 3, pp. 203–228, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. H. Föllmer and A. Schied, “Convex measures of risk and trading constraints,” Finance and Stochastics, vol. 6, no. 4, pp. 429–447, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. M. Frittelli and E. Rossaza Gianin, “Dynamic convex risk measures,” in New Riak Measures for the 21st Century, G. Szegö, Ed., pp. 227–248, John Wiley & Sons, New York, NY, USA, 2004. View at Google Scholar
  6. S. Peng, “Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations,” Science in China A: Mathematics, vol. 52, no. 7, pp. 1391–1411, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. L. G. Epstein and S. Ji, “Ambiguous volatility, possibility and utility in continuous time,” Journal of Mathematical Economics, vol. 50, pp. 269–282, 2014. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. L. G. Epstein and S. Ji, “Ambiguous volatility and asset pricing in continuous time,” Review of Financial Studies, vol. 26, no. 7, pp. 1740–1786, 2013. View at Google Scholar
  9. M. Hu, S. Ji, S. Peng, and Y. Song, “Backward stochastic differential equations driven by G-Brownian motion,” Stochastic Processes and Their Applications, vol. 124, no. 1, pp. 759–784, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  10. M. Hu, S. Ji, S. Peng, and Y. Song, “Comparison theorem, Feynman-Kac formula and Girsanov transformation for BSDEs driven by G-Brownian motion,” Stochastic Processes and Their Applications, vol. 124, no. 2, pp. 1170–1195, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  11. M. Hu, S. Ji, and S. Yang, “A stochastic recursive optimal control problem under the G-expectation framework,” Applied Mathematics & Optimization, 2014. View at Publisher · View at Google Scholar
  12. X. Xiao, “Stochastic dominance under the nonlinear expected utilities,” . In press.
  13. F. Hu, “On Cramér’s theorem for capacities,” Comptes Rendus de l'Académie des Sciences I, vol. 348, no. 17-18, pp. 1009–1013, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. S. Peng, “G-Brownian motion and dynamic risk measure under volatility uncertainty,” http://arxiv.org/abs/0711.2834.
  15. S. Peng, “A new central limit theorem under sublinear expectations,” http://arxiv.org/abs/0803.2656.
  16. F. Gao and H. Jiang, “Large deviations for stochastic differential equations driven by G-Brownian motion,” Stochastic Processes and Their Applications, vol. 120, no. 11, pp. 2212–2240, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  17. L. Ren, G-Lévy processes in finite and infinite dimensional space and related topics [Ph.D. thesis], 2012.
  18. M. Hu and S. Peng, “G-Lévy processesunder sublinear expectations,” http://arxiv.org/abs/0911.3533.
  19. F. Gao and M. Xu, “Large deviations and Moderate deviations of independent random variables under sublinear expectations,” Science China Mathematics, vol. 41, no. 4, pp. 337–352, 2011 (Chinese). View at Google Scholar