Law of large numbers under the nonlinear expectation
HTML articles powered by AMS MathViewer
- by B. Yang and H. Xiao PDF
- Proc. Amer. Math. Soc. 139 (2011), 3753-3762 Request permission
Abstract:
In this paper, we propose a class of nonlinear expectations induced by backward stochastic differential equations and reflected backward stochastic differential equations and prove the law of large numbers under the nonlinear expectation.References
- Zengjing Chen, Reg Kulperger, and Long Jiang, Jensen’s inequality for $g$-expectation. I, C. R. Math. Acad. Sci. Paris 337 (2003), no. 11, 725–730 (English, with English and French summaries). MR 2030410, DOI 10.1016/j.crma.2003.09.017
- Zengjing Chen, Reg Kulperger, and Long Jiang, Jensen’s inequality for $g$-expectation. II, C. R. Math. Acad. Sci. Paris 337 (2003), no. 12, 797–800 (English, with English and French summaries). MR 2033122, DOI 10.1016/j.crma.2003.09.037
- Jakša Cvitanić and Ioannis Karatzas, Backward stochastic differential equations with reflection and Dynkin games, Ann. Probab. 24 (1996), no. 4, 2024–2056. MR 1415239, DOI 10.1214/aop/1041903216
- N. El Karoui, C. Kapoudjian, E. Pardoux, S. Peng, and M. C. Quenez, Reflected solutions of backward SDE’s, and related obstacle problems for PDE’s, Ann. Probab. 25 (1997), no. 2, 702–737. MR 1434123, DOI 10.1214/aop/1024404416
- N. El Karoui, S. Peng, and M. C. Quenez, Backward stochastic differential equations in finance, Math. Finance 7 (1997), no. 1, 1–71. MR 1434407, DOI 10.1111/1467-9965.00022
- Long Jiang and Zeng-jing Chen, A result on the probability measures dominated by $g$-expectation, Acta Math. Appl. Sin. Engl. Ser. 20 (2004), no. 3, 507–512. MR 2086771, DOI 10.1007/s10255-004-0188-5
- Long Jiang and Zengjing Chen, On Jensen’s inequality for $g$-expectation, Chinese Ann. Math. Ser. B 25 (2004), no. 3, 401–412. MR 2086132, DOI 10.1142/S0252959904000378
- É. Pardoux and S. G. Peng, Adapted solution of a backward stochastic differential equation, Systems Control Lett. 14 (1990), no. 1, 55–61. MR 1037747, DOI 10.1016/0167-6911(90)90082-6
- Nicole El Karoui and Laurent Mazliak (eds.), Backward stochastic differential equations, Pitman Research Notes in Mathematics Series, vol. 364, Longman, Harlow, 1997. Papers from the study group held at the University of Paris VI, Paris, 1995–1996. MR 1752671
- A. N. Shiryayev, Probability, Graduate Texts in Mathematics, vol. 95, Springer-Verlag, New York, 1984. Translated from the Russian by R. P. Boas. MR 737192, DOI 10.1007/978-1-4899-0018-0
Additional Information
- B. Yang
- Affiliation: School of Mathematics and Statistics, Shandong University at Weihai, Weihai 264209, People’s Republic of China
- Email: bingyang@sdu.edu.cn
- H. Xiao
- Affiliation: School of Mathematics and Statistics, Shandong University at Weihai, Weihai 264209, People’s Republic of China
- Email: xiao_hua@sdu.edu.cn
- Received by editor(s): May 20, 2010
- Received by editor(s) in revised form: September 4, 2010
- Published electronically: February 28, 2011
- Additional Notes: The second author is the corresponding author and acknowledges the support of the National Nature Science Foundation of China (11001156, 11071144, 11026125), the Nature Science Foundation of Shandong Province (ZR2009AQ017), and the Independent Innovation Foundation of Shandong University (IIFSDU), China
- Communicated by: Edward C. Waymire
- © Copyright 2011 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 139 (2011), 3753-3762
- MSC (2010): Primary 60F05, 60G50; Secondary 60F99
- DOI: https://doi.org/10.1090/S0002-9939-2011-10814-1
- MathSciNet review: 2813405