IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v80y2010i5-6p519-526.html
   My bibliography  Save this article

Dynkin's formula under the G-expectation

Author

Listed:
  • Chen, Xiaoyan

Abstract

In 2006, Peng introduced a new kind of nonlinear expectation--G-expectation (see Peng, 2006). And he also established a theory of stochastic calculus under the G-expectation (see [4], [5] and [7]). In this paper, we will prove a nonlinear Dynkin's formula when the generator of a G-Itô's diffusion is well defined in the framework of the G-expectation.

Suggested Citation

  • Chen, Xiaoyan, 2010. "Dynkin's formula under the G-expectation," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 519-526, March.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:5-6:p:519-526
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(09)00455-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    3. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Max Nendel, 2021. "Markov chains under nonlinear expectation," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 474-507, January.
    2. Nendel, Max, 2019. "On Nonlinear Expectations and Markov Chains under Model Uncertainty," Center for Mathematical Economics Working Papers 628, Center for Mathematical Economics, Bielefeld University.
    3. Rieger, Marc Oliver, 2017. "Characterization of acceptance sets for co-monotone risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 147-152.
    4. Andres Mauricio Molina Barreto & Naoyuki Ishimura, 2023. "Remarks on a copula‐based conditional value at risk for the portfolio problem," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 30(3), pages 150-170, July.
    5. Soren Bettels & Stefan Weber, 2024. "An Integrated Approach to Importance Sampling and Machine Learning for Efficient Monte Carlo Estimation of Distortion Risk Measures in Black Box Models," Papers 2408.02401, arXiv.org, revised Jan 2025.
    6. Ji, Ronglin & Shi, Xuejun & Wang, Shijie & Zhou, Jinming, 2019. "Dynamic risk measures for processes via backward stochastic differential equations," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 43-50.
    7. Andreas H Hamel, 2018. "Monetary Measures of Risk," Papers 1812.04354, arXiv.org.
    8. Steven Kou & Xianhua Peng, 2014. "On the Measurement of Economic Tail Risk," Papers 1401.4787, arXiv.org, revised Aug 2015.
    9. Damir Filipović, 2008. "Optimal Numeraires For Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 333-336, April.
    10. Lisa R. Goldberg & Ola Mahmoud, 2014. "Drawdown: From Practice to Theory and Back Again," Papers 1404.7493, arXiv.org, revised Sep 2016.
    11. Roger J. A. Laeven & John G. M. Schoenmakers & Nikolaus F. F. Schweizer & Mitja Stadje, 2020. "Robust Multiple Stopping -- A Pathwise Duality Approach," Papers 2006.01802, arXiv.org, revised Sep 2021.
    12. Wei Chen, 2013. "Fractional G-White Noise Theory, Wavelet Decomposition for Fractional G-Brownian Motion, and Bid-Ask Pricing Application to Finance Under Uncertainty," Papers 1306.4070, arXiv.org.
    13. , & ,, 2015. "The Foster-Hart measure of riskiness for general gambles," Theoretical Economics, Econometric Society, vol. 10(1), January.
    14. Qian Lin & Frank Riedel, 2021. "Optimal consumption and portfolio choice with ambiguous interest rates and volatility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1189-1202, April.
    15. Zachary Feinstein & Birgit Rudloff, 2018. "Scalar multivariate risk measures with a single eligible asset," Papers 1807.10694, arXiv.org, revised Feb 2021.
    16. Yanhong Chen & Zachary Feinstein, 2022. "Set-valued dynamic risk measures for processes and for vectors," Finance and Stochastics, Springer, vol. 26(3), pages 505-533, July.
    17. Fei Sun & Yijun Hu, 2018. "Systemic risk measures with markets volatility," Papers 1812.06185, arXiv.org, revised Jun 2019.
    18. Mao, Tiantian & Hu, Jiuyun & Liu, Haiyan, 2018. "The average risk sharing problem under risk measure and expected utility theory," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 170-179.
    19. repec:cte:wbrepe:wb043513 is not listed on IDEAS
    20. Gilles Boevi Koumou & Georges Dionne, 2022. "Coherent Diversification Measures in Portfolio Theory: An Axiomatic Foundation," Risks, MDPI, vol. 10(11), pages 1-19, October.
    21. Rosazza Gianin, Emanuela, 2006. "Risk measures via g-expectations," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 19-34, August.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:80:y:2010:i:5-6:p:519-526. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.