IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v123y2013i2p275-299.html
   My bibliography  Save this article

A converse comparison theorem for anticipated BSDEs and related non-linear expectations

Author

Listed:
  • Yang, Zhe
  • Elliott, Robert J.

Abstract

The converse comparison theorem has received much attention in the theory of backward stochastic differential equations (BSDEs). However, no such theorem has been proved for anticipated BSDEs. In this paper, we derive a converse comparison theorem by first giving an existence and uniqueness theorem for adapted solutions of anticipated BSDEs with a stopping time and then related to (f,δ)-expectations induced by anticipated BSDEs.

Suggested Citation

  • Yang, Zhe & Elliott, Robert J., 2013. "A converse comparison theorem for anticipated BSDEs and related non-linear expectations," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 275-299.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:2:p:275-299
    DOI: 10.1016/j.spa.2012.09.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414912001998
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2012.09.006?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. Jiang, Long, 2005. "Converse comparison theorems for backward stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 71(2), pages 173-183, February.
    2. Chen, Zengjing & Peng, Shige, 2000. "A general downcrossing inequality for g-martingales," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 169-175, January.
    3. 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.
    4. Rosazza Gianin, Emanuela, 2006. "Risk measures via g-expectations," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 19-34, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xiong, Yafang & Xu, Xiaoming, 2020. "Anticipated backward stochastic differential equations with left-Lipschitz coefficient," Statistics & Probability Letters, Elsevier, vol. 163(C).
    2. Wu, Hao & Li, Xuefeng, 2021. "Converse comparison theorems for multidimensional anticipated backward stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 168(C).

    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. Zhao, Guoqing, 2009. "Lenglart domination inequalities for g-expectations," Statistics & Probability Letters, Elsevier, vol. 79(22), pages 2338-2342, November.
    2. Freddy Delbaen & Shige Peng & Emanuela Rosazza Gianin, 2010. "Representation of the penalty term of dynamic concave utilities," Finance and Stochastics, Springer, vol. 14(3), pages 449-472, September.
    3. Leitner Johannes, 2007. "Pricing and hedging with globally and instantaneously vanishing risk," Statistics & Risk Modeling, De Gruyter, vol. 25(4), pages 311-332, October.
    4. Bayraktar, Erhan & Yao, Song, 2015. "Doubly reflected BSDEs with integrable parameters and related Dynkin games," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4489-4542.
    5. Erhan Bayraktar & Song Yao, 2009. "Optimal Stopping for Non-linear Expectations," Papers 0905.3601, arXiv.org, revised Jan 2011.
    6. Jana Bielagk & Arnaud Lionnet & Gonçalo dos Reis, 2015. "Equilibrium pricing under relative performance concerns," Working Papers hal-01245812, HAL.
    7. Nicole EL KAROUI & Claudia RAVANELLI, 2008. "Cash Sub-additive Risk Measures and Interest Rate Ambiguity," Swiss Finance Institute Research Paper Series 08-09, Swiss Finance Institute.
    8. Samuel N. Cohen & Robert J. Elliott, 2008. "Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions," Papers 0810.0055, arXiv.org, revised Jan 2010.
    9. Antoon Pelsser & Mitja Stadje, 2014. "Time-Consistent And Market-Consistent Evaluations," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 25-65, January.
    10. Rosazza Gianin, Emanuela, 2006. "Risk measures via g-expectations," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 19-34, August.
    11. Nam, Kihun, 2021. "Locally Lipschitz BSDE driven by a continuous martingale a path-derivative approach," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 376-411.
    12. Dejian Tian, 2022. "Pricing principle via Tsallis relative entropy in incomplete market," Papers 2201.05316, arXiv.org, revised Oct 2022.
    13. Song, Wenjie & Wu, Panyu & Zhang, Guodong, 2021. "Jensen’s inequality for g-expectations in general filtration spaces," Statistics & Probability Letters, Elsevier, vol. 169(C).
    14. De Scheemaekere, Xavier, 2011. "A converse comparison theorem for backward stochastic differential equations with jumps," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 298-301, February.
    15. Yang Shen & Tak Kuen Siu, 2018. "A Risk-Based Approach for Asset Allocation with A Defaultable Share," Risks, MDPI, vol. 6(1), pages 1-27, February.
    16. Chen, Zengjing & Epstein, Larry G., 2022. "A central limit theorem for sets of probability measures," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 424-451.
    17. Shuxia Guo & Zhe Meng, 2023. "The Marcinkiewicz–Zygmund-Type Strong Law of Large Numbers with General Normalizing Sequences under Sublinear Expectation," Mathematics, MDPI, vol. 11(23), pages 1-21, November.
    18. Liu, Haodong & Yang, Shuzhen, 2017. "Representation and converse comparison theorems for multidimensional BSDEs," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 67-74.
    19. Ludovic Tangpi, 2018. "Concentration of dynamic risk measures in a Brownian filtration," Papers 1805.09014, arXiv.org.
    20. {L}ukasz Delong, 2010. "BSDEs with time-delayed generators of a moving average type with applications to non-monotone preferences," Papers 1008.3722, arXiv.org, revised Jul 2011.

    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:spapps:v:123:y:2013:i:2:p:275-299. 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/505572/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.