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Stochastic Analysis and Applications Volume 37, 2019 - Issue 3
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Articles

The application of multi-dimensional Jensen’s inequality for G-martingale

Yuan Bao KangSchool of Mathematics Science, Chongqing Normal University, Chongqing, ChinaCorrespondence[email protected]
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Pages 499-508 | Received 12 Nov 2018, Accepted 08 Feb 2019, Published online: 07 Apr 2019

References

  • Artzner, P., Delbaen, F., Eber, J. M., Heath, D. (1999). Coherence measures of risk. Math Finance 9(3):203–228. DOI: 10.1111/1467-9965.00068.
  • PardouxPeng, ES. (1990). Adapted solution of a backward stochastic differential equation. Syst. Control Lett. 14(1):55–61. DOI: 10.1016/0167-6911(90)90082-6.
  • Coquet, F., Hu, Y., Memin, J., Peng, S. (2002). Filtration-consistent nonlinear expectations and related g-expectations. Probab. Theory Relat. Fields 123(1):1–27. DOI: 10.1007/s004400100172.
  • Chen, Z., Epstein, L. (2002). Ambiguity, risk and asset returns in continuous time. Econometrica 70(4):1403–1443. DOI: 10.1111/1468-0262.00337.
  • El Karoui, N., Peng, S., Quenez, M. C. (1997). Backward stochastic differential equation in finance. Math. Finance 7(1):1–71. DOI: 10.1111/1467-9965.00022.
  • Peng, S. (2007). G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Itô Type. In: Benth F.E., Di Nunno G., Lindstrøm T., Øksendal B., Zhang T. eds. Stochastic Analysis and Applications. Abel Symposia, vol 2. Berlin, Heidelberg: Springer.
  • Delbaen, F. (2002). Coherent Risk Measures on General Probability Spaces. In: Sandmann K., Schönbucher P.J. eds. Advances in Finance and Stochastics. Berlin, Heidelberg: Springer.
  • Peng, S. (1997). Backward SDE and Related g-Expectations, In: Karoui Mazliak, ed. Backward Stochastic Differential Equations, Pitman Research Notes in Math. Series, No. 364, pp. 141–159.
  • Föllmer, H., Schied, A. (2002). Convex measures of risk and trading constrains. Finance Stoch. 6(4):429–447. DOI: 10.1007/s007800200072.
  • Peng, S. (2004). Nonlinear Expectations, Nonlinear Evaluations and Risk Measures. In: M. Frittelli, and Runggaldier W. eds. Stochastic Methods in Finance. Lecture Notes in Mathematics, vol 1856. Berlin, Heidelberg: Springer, pp. 165–253.
  • Peng, S. (2008). Multi-dimensional G-Brownian motion and ralated stochastic calculus under G-expectation. Stoch. Process Appl. 118(12):2223–2253. DOI: 10.1016/j.spa.2007.10.015.
  • Jia, G. (2010). On Jensen’s inequality and hölder’s inequality for g-expectation. Arch. Math. 94:489–499. DOI: 10.1007/s00013-010-0117-1.
  • ChenKulperger, Z. R., Jiang, L. (2003). Jensen’s inequality for g-expectation, part 1. C. R. Acad. Sci.Paris Ser. I 337(11):725–730. DOI: 10.1016/j.crma.2003.09.017.
  • Chen, Z., Kulperger, R., Jiang, L. (2003). Jensen’s inequality for g-expectation, part 2. C. R. Acad. Sci. Paris Ser. I 337(12):797–800. DOI: 10.1016/j.crma.2003.09.037.
  • Fan, S. (2006). Jensen’s inequality for g-expectation on convex(concave)function, chinese ann. Math. Ser. A 27(5):635–644. (in chinese).
  • Jiang, L. (2003). On jensen’s inequality of bivariate function for g-expectation. J. Shandong Univ. 38(5):13–22. (in chinese).
  • Soner, M., Touzi, N., Zhang, J. (2009). Martingale representation theorem under G-expectation. Stoch. Process. Appl., 121:265–287.
  • Song, Y. (2009). Some properties on G-evaluation and its applications to G-martingale decomposition. Sci. China Math. 54(2):287–300.

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