IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v169y2021ics0167715220302613.html

Jensen’s inequality for g-expectations in general filtration spaces

Author

Listed:
  • Song, Wenjie
  • Wu, Panyu
  • Zhang, Guodong

Abstract

In this paper, we investigate the properties of BSDEs in general filtration spaces based on the transposition solutions. We obtain a result that Jensen’s inequality holds under the g-expectation and conditional g-expectation in general filtration spaces if and only if g is independent of y and super-homogeneous in z.

Suggested Citation

  • Song, Wenjie & Wu, Panyu & Zhang, Guodong, 2021. "Jensen’s inequality for g-expectations in general filtration spaces," Statistics & Probability Letters, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:stapro:v:169:y:2021:i:c:s0167715220302613
    DOI: 10.1016/j.spl.2020.108958
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715220302613
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2020.108958?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    2. 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.
    3. Rosazza Gianin, Emanuela, 2006. "Risk measures via g-expectations," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 19-34, August.
    4. Du, Kai & Zhang, Qi, 2013. "Semi-linear degenerate backward stochastic partial differential equations and associated forward–backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1616-1637.
    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. Jiang, Long, 2009. "A necessary and sufficient condition for probability measures dominated by g-expectation," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 196-201, January.
    2. Antoon Pelsser & Mitja Stadje, 2014. "Time-Consistent And Market-Consistent Evaluations," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 25-65, January.
    3. Zhao, Guoqing, 2009. "Lenglart domination inequalities for g-expectations," Statistics & Probability Letters, Elsevier, vol. 79(22), pages 2338-2342, November.
    4. Beissner, Patrick & Rosazza Gianin, Emanuela, 2018. "The Term Structure of Sharpe Ratios and Arbitrage-Free Asset Pricing in Continuous Time," Rationality and Competition Discussion Paper Series 72, CRC TRR 190 Rationality and Competition.
    5. Yufeng Shi & Bin Teng & Sicong Wang, 2025. "Option pricing mechanisms driven by backward stochastic differential equations," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 11(1), pages 1-19, December.
    6. Hu, Feng & Chen, Zengjing, 2010. "Generalized Peng's g-expectations and related properties," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 191-195, February.
    7. Roger J. A. Laeven & Emanuela Rosazza Gianin & Marco Zullino, 2023. "Dynamic Return and Star-Shaped Risk Measures via BSDEs," Papers 2307.03447, arXiv.org, revised Jul 2023.
    8. Fujii, Masaaki & Takahashi, Akihiko, 2019. "Solving backward stochastic differential equations with quadratic-growth drivers by connecting the short-term expansions," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1492-1532.
    9. 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.
    10. Albrecht, E & Baum, Günter & Birsa, R & Bradamante, F & Bressan, A & Chapiro, A & Cicuttin, A & Ciliberti, P & Colavita, A & Costa, S & Crespo, M & Cristaudo, P & Dalla Torre, S & Diaz, V & Duic, V &, 2010. "Results from COMPASS RICH-1," Center for Mathematical Economics Working Papers 535, Center for Mathematical Economics, Bielefeld University.
    11. Chen, Zengjing & Kulperger, Reg, 2006. "Minimax pricing and Choquet pricing," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 518-528, June.
    12. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    13. 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.
    14. Chen, Zengjing & Kulperger, Reg & Wei, Gang, 2005. "A comonotonic theorem for BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 41-54, January.
    15. Attaoui, Sami & Cao, Wenbin & Duan, Xiaoman & Liu, Hening, 2021. "Optimal capital structure, ambiguity aversion, and leverage puzzles," Journal of Economic Dynamics and Control, Elsevier, vol. 129(C).
    16. Ali Lazrak, 2005. "Generalized stochastic differential utility and preference for information," Papers math/0503579, arXiv.org.
    17. Jianjun Miao, 2009. "Ambiguity, Risk and Portfolio Choice under Incomplete Information," Annals of Economics and Finance, Society for AEF, vol. 10(2), pages 257-279, November.
    18. Carole Bernard & Shaolin Ji & Weidong Tian, 2013. "An optimal insurance design problem under Knightian uncertainty," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 36(2), pages 99-124, November.
    19. Ji Huang, 2023. "A Probabilistic Solution to High-Dimensional Continuous-Time Macro and Finance Models," CESifo Working Paper Series 10600, CESifo.
    20. 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.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    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:169:y:2021:i:c:s0167715220302613. 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.