IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v173y2024ics0304414924000644.html
   My bibliography  Save this article

Stability for generalized stochastic equations

Author

Listed:
  • Andrade da Silva, F.
  • Bonotto, E.M.
  • Federson, M.

Abstract

Similarly to generalized ordinary differential equations that comprise various types of classical deterministic equations, generalized stochastic equations (GSEs) were created to contain equations involving stochastic processes. The main goal of this paper is to investigate several types of stability and boundedness for non-autonomous GSEs by means of Lyapunov functionals. We also established existence–uniqueness results for maximal and global forward solutions of GSEs and applied our result to the Ornstein–Uhlenbeck process.

Suggested Citation

  • Andrade da Silva, F. & Bonotto, E.M. & Federson, M., 2024. "Stability for generalized stochastic equations," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    • Handle: RePEc:eee:spapps:v:173:y:2024:i:c:s0304414924000644
    DOI: 10.1016/j.spa.2024.104358
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414924000644
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2024.104358?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. Márcia Federson & Jaqueline G. Mesquita & Eduard Toon, 2015. "Lyapunov theorems for measure functional differential equations via Kurzweil-equations," Mathematische Nachrichten, Wiley Blackwell, vol. 288(13), pages 1487-1511, September.
    2. Rainer Schöbel & Jianwei Zhu, 1999. "Stochastic Volatility With an Ornstein–Uhlenbeck Process: An Extension," Review of Finance, European Finance Association, vol. 3(1), pages 23-46.
    3. M. Federson & R. Grau & J. G. Mesquita, 2019. "Prolongation of solutions of measure differential equations and dynamic equations on time scales," Mathematische Nachrichten, Wiley Blackwell, vol. 292(1), pages 22-55, 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. Yingying Wang & Zhinan Xia, 2023. "Lipschitz Stability in Terms of Two Measures for Kurzweil Equations and Applications," Mathematics, MDPI, vol. 11(9), pages 1-20, April.
    2. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Working Papers hal-02946146, HAL.
    3. Damir Filipovi'c & Martin Larsson, 2017. "Polynomial Jump-Diffusion Models," Papers 1711.08043, arXiv.org, revised Jul 2019.
    4. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Finance and Stochastics, Springer, vol. 26(4), pages 733-769, October.
    5. Wang, Ning & Zhang, Yumo, 2024. "Robust asset-liability management games for n players under multivariate stochastic covariance models," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 67-98.
    6. Michael Kurz, 2018. "Closed-form approximations in derivatives pricing: The Kristensen-Mele approach," Papers 1804.08904, arXiv.org.
    7. Aït-Sahalia, Yacine & Li, Chenxu & Li, Chen Xu, 2021. "Closed-form implied volatility surfaces for stochastic volatility models with jumps," Journal of Econometrics, Elsevier, vol. 222(1), pages 364-392.
    8. Jaehyuk Choi, 2024. "Exact simulation scheme for the Ornstein-Uhlenbeck driven stochastic volatility model with the Karhunen-Lo\`eve expansions," Papers 2402.09243, arXiv.org.
    9. Nicolas Langrené & Geoffrey Lee & Zili Zhu, 2016. "Switching To Nonaffine Stochastic Volatility: A Closed-Form Expansion For The Inverse Gamma Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-37, August.
    10. Ymir Mäkinen & Juho Kanniainen & Moncef Gabbouj & Alexandros Iosifidis, 2019. "Forecasting jump arrivals in stock prices: new attention-based network architecture using limit order book data," Quantitative Finance, Taylor & Francis Journals, vol. 19(12), pages 2033-2050, December.
    11. Rehez Ahlip & Laurence A. F. Park & Ante Prodan, 2017. "Pricing currency options in the Heston/CIR double exponential jump-diffusion model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-30, March.
    12. Björn Lutz, 2010. "Pricing of Derivatives on Mean-Reverting Assets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02909-7, October.
    13. Dong-Mei Zhu & Jiejun Lu & Wai-Ki Ching & Tak-Kuen Siu, 2019. "Option Pricing Under a Stochastic Interest Rate and Volatility Model with Hidden Markovian Regime-Switching," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 555-586, February.
    14. Gerrard, Russell & Kyriakou, Ioannis & Nielsen, Jens Perch & Vodička, Peter, 2023. "On optimal constrained investment strategies for long-term savers in stochastic environments and probability hedging," European Journal of Operational Research, Elsevier, vol. 307(2), pages 948-962.
    15. Hideharu Funahashi, 2017. "Pricing derivatives with fractional volatility," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-28, March.
    16. Stefano De Marco & Peter Friz, 2013. "Varadhan's formula, conditioned diffusions, and local volatilities," Papers 1311.1545, arXiv.org, revised Jun 2016.
    17. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524, August.
    18. Eduardo Abi Jaber & Enzo Miller & Huyên Pham, 2021. "Markowitz portfolio selection for multivariate affine and quadratic Volterra models," Post-Print hal-02877569, HAL.
    19. Eduardo Abi Jaber, 2020. "The Laplace transform of the integrated Volterra Wishart process," Working Papers hal-02367200, HAL.
    20. Roger Lord, 2010. "Comment on: A Note on the Discontinuity Problem in Heston's Stochastic Volatility Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(4), pages 373-376.

    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:173:y:2024:i:c:s0304414924000644. 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.