IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v165y2015i2d10.1007_s10957-014-0625-4.html
   My bibliography  Save this article

Arrow Sufficient Conditions for Optimality of Fully Coupled Forward–Backward Stochastic Differential Equations with Applications to Finance

Author

Listed:
  • Guangchen Wang

    (Shandong University)

  • Hua Xiao

    (Shandong University)

Abstract

This paper is concerned with optimal control problems of fully coupled forward–backward stochastic differential equations on finite horizon and infinite horizon with partial information. Two sufficient conditions for optimality are established for the above problems. We demonstrate their applications by four illustrative examples in the framework of cash management, risk minimizing, and linear-quadratic optimal control problems. These examples are explicitly solved based on the sufficient conditions and the optimal filtering of forward–backward stochastic differential equations derived in this paper.

Suggested Citation

  • Guangchen Wang & Hua Xiao, 2015. "Arrow Sufficient Conditions for Optimality of Fully Coupled Forward–Backward Stochastic Differential Equations with Applications to Finance," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 639-656, May.
    • Handle: RePEc:spr:joptap:v:165:y:2015:i:2:d:10.1007_s10957-014-0625-4
    DOI: 10.1007/s10957-014-0625-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-014-0625-4
    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/s10957-014-0625-4?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. Antonelli, Fabio & Barucci, Emilio & Mancino, Maria Elvira, 2001. "Asset pricing with a forward-backward stochastic differential utility," Economics Letters, Elsevier, vol. 72(2), pages 151-157, August.
    2. Bensoussan, Alain & Chutani, Anshuman & Sethi, Suresh, 2009. "Optimal Cash Management Under Uncertainty," MPRA Paper 19896, University Library of Munich, Germany.
    3. Xiong, Jie, 2008. "An Introduction to Stochastic Filtering Theory," OUP Catalogue, Oxford University Press, number 9780199219704.
    4. Rosazza Gianin, Emanuela, 2006. "Risk measures via g-expectations," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 19-34, August.
    5. Peng, Shige & Shi, Yufeng, 2000. "Infinite horizon forward-backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 85(1), pages 75-92, January.
    6. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
    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. Zhang, Shen & Xu, Juanjuan & Zhang, Huanshui, 2024. "Decentralized control of forward and backward stochastic difference system with nested asymmetric information," Applied Mathematics and Computation, Elsevier, vol. 478(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. Huang, Jianhui & Wang, Guangchen & Wu, Zhen, 2010. "Optimal premium policy of an insurance firm: Full and partial information," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 208-215, October.
    2. Haiyang Wang & Zhen Wu, 2014. "Partially Observed Time-Inconsistency Recursive Optimization Problem and Application," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 664-687, May.
    3. Yannacopoulos, Athanasios N., 2008. "Rational expectations models: An approach using forward-backward stochastic differential equations," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 251-276, February.
    4. Antoon Pelsser & Mitja Stadje, 2014. "Time-Consistent And Market-Consistent Evaluations," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 25-65, January.
    5. Stadje, Mitja, 2010. "Extending dynamic convex risk measures from discrete time to continuous time: A convergence approach," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 391-404, December.
    6. Hisashi Nakamura & Wataru Nozawa & Akihiko Takahashi, 2009. "Macroeconomic Implications of Term Structures of Interest Rates Under Stochastic Differential Utility with Non-Unitary EIS," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 16(3), pages 231-263, September.
    7. 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.
    8. Kohlmann, Michael, 1999. "(Reflected) Backward Stochastic Differential Equations and Contingent Claims," CoFE Discussion Papers 99/10, University of Konstanz, Center of Finance and Econometrics (CoFE).
    9. Sang Byung Seo & Jessica A. Wachter, 2019. "Option Prices in a Model with Stochastic Disaster Risk," Management Science, INFORMS, vol. 65(8), pages 3449-3469, August.
    10. Xiangyu Cui & Xun Li & Duan Li & Yun Shi, 2014. "Time Consistent Behavior Portfolio Policy for Dynamic Mean-Variance Formulation," Papers 1408.6070, arXiv.org, revised Aug 2015.
    11. Michael Monoyios & Oleksii Mostovyi, 2022. "Stability of the Epstein-Zin problem," Papers 2208.09895, arXiv.org, revised Apr 2023.
    12. Fahrenwaldt, Matthias Albrecht & Jensen, Ninna Reitzel & Steffensen, Mogens, 2020. "Nonrecursive separation of risk and time preferences," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 95-108.
    13. Dirk Becherer & Wilfried Kuissi-Kamdem & Olivier Menoukeu-Pamen, 2023. "Optimal consumption with labor income and borrowing constraints for recursive preferences," Working Papers hal-04017143, HAL.
    14. Dominika Czyz & Karolina Safarzynska, 2023. "Catastrophic Damages and the Optimal Carbon Tax Under Loss Aversion," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 85(2), pages 303-340, June.
    15. Maroulas, Vasileios & Xiong, Jie, 2013. "Large deviations for optimal filtering with fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2340-2352.
    16. Jaroslav Borovička & Lars Peter Hansen & José A. Scheinkman, 2016. "Misspecified Recovery," Journal of Finance, American Finance Association, vol. 71(6), pages 2493-2544, December.
    17. Aït-Sahalia, Yacine & Matthys, Felix, 2019. "Robust consumption and portfolio policies when asset prices can jump," Journal of Economic Theory, Elsevier, vol. 179(C), pages 1-56.
    18. Maroulas, Vasileios & Pan, Xiaoyang & Xiong, Jie, 2020. "Large deviations for the optimal filter of nonlinear dynamical systems driven by Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 203-231.
    19. Chabakauri, Georgy, 2010. "Asset pricing with heterogeneous investors and portfolio constraints," LSE Research Online Documents on Economics 43142, London School of Economics and Political Science, LSE Library.
    20. Isaenko, Sergei, 2008. "The term structure of interest rates in a pure exchange economy where investors have heterogeneous recursive preferences," The Quarterly Review of Economics and Finance, Elsevier, vol. 48(3), pages 457-481, August.

    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:joptap:v:165:y:2015:i:2:d:10.1007_s10957-014-0625-4. 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.