IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v148y2022icp278-298.html
   My bibliography  Save this article

Backward stochastic differential equations with regime-switching and sublinear expectations

Author

Listed:
  • Dela Vega, Engel John C.
  • Elliott, Robert J.

Abstract

This paper introduces a backward stochastic differential equation driven by both Brownian motion and a Markov chain (BSDEBM). Regime-switching is also incorporated through its driver. The existence and uniqueness of the solution of the BSDEBM are proved. A comparison theorem is also derived. Filtration consistent sublinear expectations are defined and characterized as solutions to the BSDEBM. The bid and ask prices are then represented using sublinear expectations.

Suggested Citation

  • Dela Vega, Engel John C. & Elliott, Robert J., 2022. "Backward stochastic differential equations with regime-switching and sublinear expectations," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 278-298.
    • Handle: RePEc:eee:spapps:v:148:y:2022:i:c:p:278-298
    DOI: 10.1016/j.spa.2022.02.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414922000564
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2022.02.012?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. Anne Eyraud-Loisel, 2005. "Backward stochastic differential equations with enlarged filtration: Option hedging of an insider trader in a financial market with jumps," Post-Print hal-01298905, HAL.
    2. Na Li & Yuan Wang & Zhen Wu, 2018. "An Indefinite Stochastic Linear Quadratic Optimal Control Problem with Delay and Related Forward–Backward Stochastic Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 722-744, November.
    3. Dilip B. Madan & Alexander Cherny, 2010. "Markets As A Counterparty: An Introduction To Conic Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(08), pages 1149-1177.
    4. 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.
    5. Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
    6. 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.
    7. 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.
    8. Eyraud-Loisel, Anne, 2005. "Backward stochastic differential equations with enlarged filtration: Option hedging of an insider trader in a financial market with jumps," Stochastic Processes and their Applications, Elsevier, vol. 115(11), pages 1745-1763, November.
    9. K. Bahlali & M. Eddahbi & E. Essaky, 2003. "BSDE associated with Lévy processes and application to PDIE," International Journal of Stochastic Analysis, Hindawi, vol. 16, pages 1-17, January.
    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. Leippold, Markus & Schärer, Steven, 2017. "Discrete-time option pricing with stochastic liquidity," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 1-16.
    2. Max Nendel, 2021. "Markov chains under nonlinear expectation," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 474-507, January.
    3. Nendel, Max, 2019. "On Nonlinear Expectations and Markov Chains under Model Uncertainty," Center for Mathematical Economics Working Papers 628, Center for Mathematical Economics, Bielefeld University.
    4. Lorenc Kapllani & Long Teng, 2020. "Deep learning algorithms for solving high dimensional nonlinear backward stochastic differential equations," Papers 2010.01319, arXiv.org, revised Jun 2022.
    5. Tomasz R. Bielecki & Igor Cialenco & Tao Chen, 2014. "Dynamic Conic Finance via Backward Stochastic Difference Equations," Papers 1412.6459, arXiv.org, revised Dec 2014.
    6. Bouchard, Bruno & Elie, Romuald, 2008. "Discrete-time approximation of decoupled Forward-Backward SDE with jumps," Stochastic Processes and their Applications, Elsevier, vol. 118(1), pages 53-75, January.
    7. Wei Chen, 2013. "Fractional G-White Noise Theory, Wavelet Decomposition for Fractional G-Brownian Motion, and Bid-Ask Pricing Application to Finance Under Uncertainty," Papers 1306.4070, arXiv.org.
    8. Madan, Dilip & Pistorius, Martijn & Stadje, Mitja, 2016. "Convergence of BSΔEs driven by random walks to BSDEs: The case of (in)finite activity jumps with general driver," Stochastic Processes and their Applications, Elsevier, vol. 126(5), pages 1553-1584.
    9. Engel John C. Dela Vega & Robert J. Elliott, 2021. "A stochastic control approach to bid-ask price modelling," Papers 2112.02368, arXiv.org.
    10. Dilip B. Madan, 2016. "Benchmarking in two price financial markets," Annals of Finance, Springer, vol. 12(2), pages 201-219, May.
    11. Dilip B. Madan & Wim Schoutens & King Wang, 2017. "Measuring And Monitoring The Efficiency Of Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-32, December.
    12. Fontana, Claudio, 2018. "The strong predictable representation property in initially enlarged filtrations under the density hypothesis," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 1007-1033.
    13. Martin Herdegen & Cosimo Munari, 2023. "An elementary proof of the dual representation of Expected Shortfall," Papers 2306.14506, arXiv.org.
    14. Leitner Johannes, 2007. "Pricing and hedging with globally and instantaneously vanishing risk," Statistics & Risk Modeling, De Gruyter, vol. 25(4/2007), pages 1-22, October.
    15. 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.
    16. Ali Lazrak, 2005. "Generalized stochastic differential utility and preference for information," Papers math/0503579, arXiv.org.
    17. Akihiro Kaneko, 2023. "Multi-stage Euler-Maruyama methods for backward stochastic differential equations driven by continuous-time Markov chains," Papers 2311.08826, arXiv.org, revised Nov 2023.
    18. Jiang Wu & Fucheng Liao & Masayoshi Tomizuka, 2017. "Optimal preview control for a linear continuous-time stochastic control system in finite-time horizon," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(1), pages 129-137, January.
    19. Hansjörg Albrecher & Karl‐Theodor Eisele & Mogens Steffensen & Mario V. Wüthrich, 2022. "On the cost‐of‐capital rate under incomplete market valuation," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(4), pages 1139-1158, December.
    20. Niushan Gao & Cosimo Munari, 2020. "Surplus-Invariant Risk Measures," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1342-1370, November.

    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:148:y:2022:i:c:p:278-298. 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.