IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v321y2018icp577-592.html
   My bibliography  Save this article

Linear-quadratic partially observed forward–backward stochastic differential games and its application in finance

Author

Listed:
  • Wu, Zhen
  • Zhuang, Yi

Abstract

This paper is concerned with a partially observed linear-quadratic game problem driven by forward–backward stochastic differential equations where the forward diffusion coefficients do not contain control variables and the control domains are not necessarily convex. The drift term of the observation equation is linear with respect to the state, and there is correlated noise between the state and the observation equation. By virtue of the classical spike variational method and the backward separation technique, we derive a necessary and a sufficient condition of the stochastic differential game problem. Then we obtain filtering equations and present a feedback representation form of the equilibrium point through Riccati equations. As a practical application, we solve a partial information investment problem involving g-expectation as a convex risk measurement and give the numerical simulation to show the explicit investment strategy and illustrate some reasonable phenomena influenced by common financial parameters.

Suggested Citation

  • Wu, Zhen & Zhuang, Yi, 2018. "Linear-quadratic partially observed forward–backward stochastic differential games and its application in finance," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 577-592.
    • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:577-592
    DOI: 10.1016/j.amc.2017.11.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630031730797X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.11.015?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. 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. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    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. Lakner, Peter, 1995. "Utility maximization with partial information," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 247-273, April.
    5. Bernt Øksendal & Agnès Sulem, 2014. "Forward–Backward Stochastic Differential Games and Stochastic Control under Model Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 22-55, April.
    6. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    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. Wang, Guangchen & Wang, Wencan & Yan, Zhiguo, 2021. "Linear quadratic control of backward stochastic differential equation with partial information," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    2. Jiang, Yan & Zhai, Junyong, 2019. "Observer-based stabilization of sector-bounded nonlinear stochastic systems in the presence of intermittent measurements," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 740-752.

    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. 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.
    2. Jana Bielagk & Arnaud Lionnet & Gonçalo dos Reis, 2015. "Equilibrium pricing under relative performance concerns," Working Papers hal-01245812, HAL.
    3. 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.
    4. Tak Siu, 2012. "A BSDE approach to risk-based asset allocation of pension funds with regime switching," Annals of Operations Research, Springer, vol. 201(1), pages 449-473, December.
    5. Jakub Trybuła & Dariusz Zawisza, 2019. "Continuous-Time Portfolio Choice Under Monotone Mean-Variance Preferences—Stochastic Factor Case," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 966-987, August.
    6. Stadje, M.A. & Pelsser, A., 2014. "Time-Consistent and Market-Consistent Evaluations (Revised version of 2012-086)," Discussion Paper 2014-002, Tilburg University, Center for Economic Research.
    7. Antoon Pelsser & Mitja Stadje, 2014. "Time-Consistent And Market-Consistent Evaluations," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 25-65, January.
    8. Rosazza Gianin, Emanuela, 2006. "Risk measures via g-expectations," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 19-34, August.
    9. Roger J. A. Laeven & Mitja Stadje, 2014. "Robust Portfolio Choice and Indifference Valuation," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1109-1141, November.
    10. Samuel N. Cohen & Tanut Treetanthiploet, 2019. "Gittins' theorem under uncertainty," Papers 1907.05689, arXiv.org, revised Jun 2021.
    11. Eduard Kromer & Ludger Overbeck, 2017. "DIFFERENTIABILITY OF BSVIEs AND DYNAMIC CAPITAL ALLOCATIONS," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1-26, November.
    12. 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.
    13. Alessandro Calvia & Emanuela Rosazza Gianin, 2019. "Risk measures and progressive enlargement of filtration: a BSDE approach," Papers 1904.13257, arXiv.org, revised Mar 2020.
    14. A. Jobert & L. C. G. Rogers, 2008. "Valuations And Dynamic Convex Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 1-22, January.
    15. Max Nendel, 2021. "Markov chains under nonlinear expectation," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 474-507, January.
    16. Jana Bielagk & Arnaud Lionnet & Goncalo Dos Reis, 2015. "Equilibrium pricing under relative performance concerns," Papers 1511.04218, arXiv.org, revised Feb 2017.
    17. Zachary Feinstein & Birgit Rudloff, 2018. "Scalar multivariate risk measures with a single eligible asset," Papers 1807.10694, arXiv.org, revised Feb 2021.
    18. Schuhmacher, Frank & Eling, Martin, 2012. "A decision-theoretic foundation for reward-to-risk performance measures," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 2077-2082.
    19. Wentao Hu & Cuixia Chen & Yufeng Shi & Ze Chen, 2022. "A Tail Measure With Variable Risk Tolerance: Application in Dynamic Portfolio Insurance Strategy," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 831-874, June.
    20. Fei Sun & Jingchao Li & Jieming Zhou, 2018. "Dynamic risk measures with fluctuation of market volatility under Bochne-Lebesgue space," Papers 1806.01166, arXiv.org, revised Mar 2024.

    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:apmaco:v:321:y:2018:i:c:p:577-592. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.