The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. Ph. Briand, F. Coquet, Y. Hu, J. Memin and S.G. Peng. A converse comparison theorem for BSDEs and related properties of g-expectation. Electron. Comm. Probab. 5 (2000), 101--117 (electronic). MR1781845 (2001h:60105)
  2. Ph. Briand, B. Delyon, Y. Hu, E. Pardoux and L. Stoica. Lp solutions of backward stochastic differential equations. Stochastic Process. Appl. 108 (2003), no. 1, 109--129. MR2008603 (2005c:60073)
  3. Ph. Briand, J.P. Lepeltier and J. San Martin. One-dimensional backward stochastic differential equations whose coefficient is monotonic in y and non-Lipschitz in z. Bernoulli 13 (2007), no. 1, 80--91. MR2307395 (2007k:60190)
  4. Z.J. Chen, R. Kulperger and L. Jiang. Jensen's inequality for g-expectation. I. C. R. Math. Acad. Sci. Paris 337 (2003), no. 11, 725--730. MR2030410 (2004k:60162)
  5. S.J. Fan. Jensen's inequality for g-expectation on convex (concave) function. (Chinese) Chinese Ann. Math. Ser. A 27 (2006), no. 5, 635--644; translation in Chinese J. Contemp. Math. 27 (2006), no. 4, 401--412 (2007) MR2266069 (2008e:60041)
  6. S.J. Fan. A relationship between the conditional g-evaluation system and the generator g and its applications. Acta Math. Sin. (Engl. Ser.) 23 (2007), no. 8, 1427--1434. MR2320749 (2008g:60179)
  7. S.J. Fan and J.H. Hu. A limit theorem for solutions to BSDEs in the space of processes. Statist. Probab. Lett. 78 (2008), no. 8, 1024--1033. MR2418920 (2009f:60071)
  8. S.J. Fan and L. Jiang. Existence and uniqueness result for a backward stochastic differential equation whose generator is Lipschitz continuous in y and uniformly continuous in z. Journal of Applied Mathematics and Computing, 2010. DOI:10.1007/s12190-010-0384-9.
  9. S.J. Fan and L. Jiang. A representation theorem for generators of BSDEs with continuous linear-growth generators in the space of processes. J. Comput. Appl. Math. 235 (2010), no. 3, 686--695. MR2719808
  10. G. Jia. Backward stochastic differential equations, g-expectations and related semilinear PDEs. PH.D Thesis, ShanDong University, China, 2008.
  11. L. Jiang and Z.J. Chen. On Jensen's inequality for g-expectation. Chinese Ann. Math. Ser. B 25 (2004), no. 3, 401--412. MR2086132 (2005h:60168)
  12. L. Jiang. Some results on the uniqueness of generators of backward stochastic differential equations. C. R. Math. Acad. Sci. Paris 338 (2004), no. 7, 575--580. MR2057033 (2005e:60141)
  13. L. Jiang. Converse comparison theorems for backward stochastic differential equations. Statist. Probab. Lett. 71 (2005), no. 2, 173--183. MR2126773 (2005j:60116)
  14. L. Jiang. Representation theorems for generators of backward stochastic differential equations. C. R. Math. Acad. Sci. Paris 340 (2005), no. 2, 161--166. MR2116776 (2005j:60125)
  15. L. Jiang. Representation theorems for generators of backward stochastic differential equations and their applications. Stochastic Process. Appl. 115 (2005), no. 12, 1883--1903. MR2178500 (2006g:60084)
  16. L. Jiang. Nonlinear expectation--g-expectation theory and its applications in finance. PH.D Thesis, ShanDong University, China, 2005.
  17. L. Jiang. Limit theorem and uniqueness theorem of backward stochastic differential equations. Sci. China Ser. A 49 (2006), no. 10, 1353--1362. MR2287264 (2008c:60053)
  18. L. Jiang. Convexity, translation invariance and subadditivity for g-expectations and related risk measures. Ann. Appl. Probab. 18 (2008), no. 1, 245--258. MR2380898 (2009f:60079)
  19. J.P. Lepeltier and J. San Martin. Backward stochastic differential equations with continuous coefficient. Statist. Probab. Lett. 32 (1997), no. 4, 425--430. MR1602231 (98j:60082)
  20. Y.C. Liu, L. Jiang and Y.Y. Xu. A local limit theorem for solutions of BSDEs with Mao's non-Lipschitz generator. Acta Math. Appl. Sin. Engl. Ser. 24 (2008), no. 2, 329--336. MR2411506(2009f:60072)
  21. X.R. Mao. Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients. Stochastic Process. Appl. 58 (1995), no. 2, 281--292. MR1348379 (96f:60099)
  22. E. Pardoux and S.G. Peng. Adapted solution of a backward stochastic differential equation. Systems Control Lett. 14 (1990), no. 1, 55--61. MR1037747 (91e:60171)


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.