Skip to main content

Advertisement

SpringerLink
Log in

Martingale Inequalities under G-Expectation and Their Applications

  • Published:
Acta Mathematica Scientia Aims and scope Submit manuscript

Abstract

In this paper, we study the martingale inequalities under G-expectation and their applications. To this end, we introduce a new kind of random time, called G-stopping time, and then investigate the properties of a G-martingale (supermartingale) such as the optional sampling theorem and upcrossing inequalities. With the help of these properties, we can show the martingale convergence property under G-expectation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Chung K L. A Course in Probability Theory. New York: Academic Press, 1974

    MATH  Google Scholar 

  2. Denis L, Hu M, Peng S. Function spaces and capacity related to a sublinear expectation: application to G-Brownian motion pathes. Potential Anal, 2011, 34: 139–161

    Article  MathSciNet  Google Scholar 

  3. Hu M, Ji S, Peng S, et al. Backward stochastic differential equations driven by G-Brownian motion. Stochastic Processes and their Applications, 2014, 124: 759–784

    Article  MathSciNet  Google Scholar 

  4. Hu M, Peng S. Extended conditional G-expectations and related stopping times. arXiv:1309.3829v1, 2013

  5. Karatzas I, Shreve S E. Brownian Motion and Stochastic Calculus. New York: Springer, 1991

    MATH  Google Scholar 

  6. Li H, Peng S, Song Y. Supermartingale decomposition theorem under G-expectation. Electron J Probab, 2018, 23: 1–20

    Article  MathSciNet  Google Scholar 

  7. Li H. Optimal stopping under G-expectation. arXiv:1812.08626, 2018

  8. Peng S. G-expectation, G-Brownian Motion and Related Stochastic Calculus of Itô type. Stochastic analysis and applications, 2007, Abel Symp, 2: 541–567

    Article  Google Scholar 

  9. Peng S. Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation. Stochastic Processes and their Applications, 2008, 118(12): 2223–2253

    Article  MathSciNet  Google Scholar 

  10. Peng S. Nonlinear expectations and stochastic calculus under uncertainty. arXiv:1002.4546v1, 2010

  11. Song Y. Some properties on G-evaluation and its applications to G-martingale decomposition. Science China Mathematics, 2011, 54: 287–300

    Article  MathSciNet  Google Scholar 

  12. Song Y. Properties of hitting times for G-martingales and their applications. Stochastic Processes and their Applications, 2011, 121: 1770–2784

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Mathematical Economics, Bielefeld University, Bielefeld, 33615, Germany

    Hanwu Li

Authors
  1. Hanwu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hanwu Li.

Additional information

The author is supported by the German Research Foundation (DFG) via CRC 1283.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, H. Martingale Inequalities under G-Expectation and Their Applications. Acta Math Sci 41, 349–360 (2021). https://doi.org/10.1007/s10473-021-0201-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10473-021-0201-6

Key words

2010 MR Subject Classification

Search

Navigation