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Martingale characterization of G-Brownian motion

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  • Xu, Jing
  • Zhang, Bo

Abstract

In this paper, we study the martingale characterization of G-Brownian motion, which was defined by Peng (cf. http://abelsymposium.no/symp2005/preprints/peng.pdf) in 2006. As an application, we present a method for constructing a G-Brownian motion using a Markov chain. Furthermore, we obtain the representation theorem for some special symmetric martingales in the G-framework.

Suggested Citation

  • Xu, Jing & Zhang, Bo, 2009. "Martingale characterization of G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 232-248, January.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:1:p:232-248
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    References listed on IDEAS

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    1. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    2. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    3. Jon Danielsson & Casper G. De Vries, 2000. "Value-at-Risk and Extreme Returns," Annals of Economics and Statistics, GENES, issue 60, pages 239-270.
    4. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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    Cited by:

    1. Li, Xinpeng & Peng, Shige, 2011. "Stopping times and related Itô's calculus with G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1492-1508, July.
    2. Ren, Yong & Hu, Lanying, 2011. "A note on the stochastic differential equations driven by G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 580-585, May.
    3. Gao, Fuqing, 2009. "Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3356-3382, October.
    4. Soner, H. Mete & Touzi, Nizar & Zhang, Jianfeng, 2011. "Martingale representation theorem for the G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 265-287, February.
    5. Marcel Nutz & H. Mete Soner, 2010. "Superhedging and Dynamic Risk Measures under Volatility Uncertainty," Papers 1011.2958, arXiv.org, revised Jun 2012.
    6. Erhan Bayraktar & Alexander Munk, 2014. "Comparing the $G$-Normal Distribution to its Classical Counterpart," Papers 1407.5139, arXiv.org, revised Dec 2014.

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