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Girsanov’s formula for G-Brownian motion

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  • Osuka, Emi

Abstract

In this paper, we establish Girsanov’s formula for G-Brownian motion. Peng (2007, 2008) [7,8] constructed G-Brownian motion on the space of continuous paths under a sublinear expectation called G-expectation; as obtained by Denis et al. (2011) [2], G-expectation is represented as the supremum of linear expectations with respect to martingale measures of a certain class. Our argument is based on this representation with an enlargement of the associated class of martingale measures, and on Girsanov’s formula for martingales in the classical stochastic analysis. The methodology differs from that of Xu et al. (2011) [13], and applies to the multidimensional G-Brownian motion.

Suggested Citation

  • Osuka, Emi, 2013. "Girsanov’s formula for G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1301-1318.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:4:p:1301-1318
    DOI: 10.1016/j.spa.2012.12.009
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    References listed on IDEAS

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    1. 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.
    2. Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
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    Cited by:

    1. Biagini, Francesca & Mancin, Jacopo & Brandis, Thilo Meyer, 2019. "Robust mean–variance hedging via G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1287-1325.
    2. Erhan Bayraktar & Alexander Munk, 2014. "An $\alpha$-stable limit theorem under sublinear expectation," Papers 1409.7960, arXiv.org, revised Jun 2016.
    3. Jaehyun Kim & Hyungbin Park, 2024. "Long-term decomposition of robust pricing kernels under G-expectation," Papers 2409.00535, arXiv.org.
    4. Francesca Biagini & Jacopo Mancin & Thilo Meyer Brandis, 2016. "Robust Mean-Variance Hedging via G-Expectation," Papers 1602.05484, arXiv.org, revised Aug 2016.
    5. Guomin Liu, 2021. "Girsanov Theorem for G-Brownian Motion: The Degenerate Case," Journal of Theoretical Probability, Springer, vol. 34(1), pages 125-140, March.
    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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