IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v31y2018i1d10.1007_s10959-016-0705-5.html
   My bibliography  Save this article

On the Representation for Dynamically Consistent Nonlinear Evaluations: Uniformly Continuous Case

Author

Listed:
  • Shiqiu Zheng

    (Beijing University of Technology
    North China University of Science and Technology)

  • Shoumei Li

    (Beijing University of Technology)

Abstract

A system of dynamically consistent nonlinear evaluation ( $${\mathcal {F}}$$ F -evaluation) provides an ideal characterization for the dynamical behaviors of risk measures and the pricing of contingent claims. The purpose of this paper is to study the representation for the $${\mathcal {F}}$$ F -evaluation by the solution of a backward stochastic differential equation (BSDE). Under a general domination condition, we prove that any $${\mathcal {F}}$$ F -evaluation can be represented by the solution of a BSDE with a generator which is Lipschitz in y and uniformly continuous in z.

Suggested Citation

  • Shiqiu Zheng & Shoumei Li, 2018. "On the Representation for Dynamically Consistent Nonlinear Evaluations: Uniformly Continuous Case," Journal of Theoretical Probability, Springer, vol. 31(1), pages 119-158, March.
  • Handle: RePEc:spr:jotpro:v:31:y:2018:i:1:d:10.1007_s10959-016-0705-5
    DOI: 10.1007/s10959-016-0705-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-016-0705-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10959-016-0705-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Lepeltier, J. P. & San Martin, J., 1997. "Backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 425-430, April.
    2. Cohen, Samuel N., 2012. "Representing filtration consistent nonlinear expectations as g-expectations in general probability spaces," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1601-1626.
    3. Royer, Manuela, 2006. "Backward stochastic differential equations with jumps and related non-linear expectations," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1358-1376, October.
    4. Jia, Guangyan, 2010. "Backward stochastic differential equations with a uniformly continuous generator and related g-expectation," Stochastic Processes and their Applications, Elsevier, vol. 120(11), pages 2241-2257, November.
    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. Fan, ShengJun, 2016. "Existence of solutions to one-dimensional BSDEs with semi-linear growth and general growth generators," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 7-15.
    2. Sheng Jun Fan, 2018. "Existence, Uniqueness and Stability of $$L^1$$ L 1 Solutions for Multidimensional Backward Stochastic Differential Equations with Generators of One-Sided Osgood Type," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1860-1899, September.
    3. Fan, ShengJun, 2016. "Bounded solutions, Lp(p>1) solutions and L1 solutions for one dimensional BSDEs under general assumptions," Stochastic Processes and their Applications, Elsevier, vol. 126(5), pages 1511-1552.
    4. M. Nabil Kazi-Tani & Dylan Possamai & Chao Zhou, 2014. "Quadratic BSDEs with jumps: related non-linear expectations," Papers 1403.2730, arXiv.org.
    5. Zhou, Guangshuo & Du, Fengjiao & Fan, Shengjun, 2024. "Invariant representation for generators of general time interval quadratic BSDEs under stochastic growth conditions," Statistics & Probability Letters, Elsevier, vol. 205(C).
    6. Fujii, Masaaki & Takahashi, Akihiko, 2018. "Quadratic–exponential growth BSDEs with jumps and their Malliavin’s differentiability," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 2083-2130.
    7. Samuel N. Cohen & Victor Fedyashov, 2014. "Ergodic BSDEs with jumps and time dependence," Papers 1406.4329, arXiv.org, revised Nov 2015.
    8. Xiao, Lishun & Fan, Shengjun, 2017. "A representation theorem for generators of BSDEs with general growth generators in y and its applications," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 297-305.
    9. Antonis Papapantoleon & Dylan Possamai & Alexandros Saplaouras, 2016. "Existence and uniqueness results for BSDEs with jumps: the whole nine yards," Papers 1607.04214, arXiv.org, revised Nov 2018.
    10. Zhang, Wei & Jiang, Long, 2021. "Solutions of BSDEs with a kind of non-Lipschitz coefficients driven by G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 171(C).
    11. Luis Escauriaza & Daniel C. Schwarz & Hao Xing, 2020. "Radner equilibrium and systems of quadratic BSDEs with discontinuous generators," Papers 2008.03500, arXiv.org, revised May 2021.
    12. Cao, Guilan & He, Kai, 2007. "Successive approximation of infinite dimensional semilinear backward stochastic evolution equations with jumps," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1251-1264, September.
    13. Qun Shi, 2021. "Generalized Mean-Field Fractional BSDEs With Non-Lipschitz Coefficients," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(3), pages 1-77, June.
    14. Fan, Xiliang & Ren, Yong & Zhu, Dongjin, 2010. "A note on the doubly reflected backward stochastic differential equations driven by a Lévy process," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 690-696, April.
    15. Possamaï, Dylan, 2013. "Second order backward stochastic differential equations under a monotonicity condition," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1521-1545.
    16. Roxana Dumitrescu & Marie-Claire Quenez & Agnès Sulem, 2015. "Optimal Stopping for Dynamic Risk Measures with Jumps and Obstacle Problems," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 219-242, October.
    17. Perninge, Magnus, 2024. "Optimal stopping of BSDEs with constrained jumps and related zero-sum games," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    18. Jing, Shuai, 2013. "Regularity properties of viscosity solutions of integro-partial differential equations of Hamilton–Jacobi–Bellman type," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 300-328.
    19. Safa Alsheyab & Tahir Choulli, 2021. "Reflected backward stochastic differential equations under stopping with an arbitrary random time," Papers 2107.11896, arXiv.org.
    20. Choukroun, Sébastien & Cosso, Andrea & Pham, Huyên, 2015. "Reflected BSDEs with nonpositive jumps, and controller-and-stopper games," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 597-633.

    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:spr:jotpro:v:31:y:2018:i:1:d:10.1007_s10959-016-0705-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.