IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v126y2016i10p3202-3234.html
   My bibliography  Save this article

Finite difference schemes for linear stochastic integro-differential equations

Author

Listed:
  • Dareiotis, Konstantinos
  • Leahy, James-Michael

Abstract

We study the rate of convergence of an explicit and an implicit–explicit finite difference scheme for linear stochastic integro-differential equations of parabolic type arising in non-linear filtering of jump–diffusion processes. We show that the rate is of order one in space and order one-half in time.

Suggested Citation

  • Dareiotis, Konstantinos & Leahy, James-Michael, 2016. "Finite difference schemes for linear stochastic integro-differential equations," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 3202-3234.
  • Handle: RePEc:eee:spapps:v:126:y:2016:i:10:p:3202-3234
    DOI: 10.1016/j.spa.2016.04.025
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414916300485
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spa.2016.04.025?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. Rama Cont & Ekaterina Voltchkova, 2005. "A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models," Post-Print halshs-00445645, HAL.
    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. Alipour, Sahar & Mirzaee, Farshid, 2020. "An iterative algorithm for solving two dimensional nonlinear stochastic integral equations: A combined successive approximations method with bilinear spline interpolation," Applied Mathematics and Computation, Elsevier, vol. 371(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. Lukas Gonon & Christoph Schwab, 2021. "Deep ReLU network expression rates for option prices in high-dimensional, exponential Lévy models," Finance and Stochastics, Springer, vol. 25(4), pages 615-657, October.
    2. Song-Ping Zhu & Xin-Jiang He, 2018. "A hybrid computational approach for option pricing," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-16, September.
    3. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
    4. Moustapha Pemy, 2018. "Explicit Solutions for Optimal Resource Extraction Problems under Regime Switching L\'evy Models," Papers 1806.06105, arXiv.org.
    5. Xu, Guoping & Zheng, Harry, 2010. "Basket options valuation for a local volatility jump-diffusion model with the asymptotic expansion method," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 415-422, December.
    6. Cl'ement M'enass'e & Peter Tankov, 2015. "Asymptotic indifference pricing in exponential L\'evy models," Papers 1502.03359, arXiv.org, revised Feb 2015.
    7. Ron Chan & Simon Hubbert, 2014. "Options pricing under the one-dimensional jump-diffusion model using the radial basis function interpolation scheme," Review of Derivatives Research, Springer, vol. 17(2), pages 161-189, July.
    8. Genin, Adrien & Tankov, Peter, 2020. "Optimal importance sampling for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 20-46.
    9. Bilel Jarraya & Abdelfettah Bouri, 2013. "A Theoretical Assessment on Optimal Asset Allocations in Insurance Industry," International Journal of Finance & Banking Studies, Center for the Strategic Studies in Business and Finance, vol. 2(4), pages 30-44, October.
    10. Hagspiel, Verena & Huisman, Kuno J.M. & Kort, Peter M. & Lavrutich, Maria N. & Nunes, Cláudia & Pimentel, Rita, 2020. "Technology adoption in a declining market," European Journal of Operational Research, Elsevier, vol. 285(1), pages 380-392.
    11. Fouladi, Somayeh & Dahaghin, Mohammad Shafi, 2022. "Numerical investigation of the variable-order fractional Sobolev equation with non-singular Mittag–Leffler kernel by finite difference and local discontinuous Galerkin methods," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    12. Nicola Bruti-Liberati & Eckhard Platen, 2007. "Approximation of jump diffusions in finance and economics," Computational Economics, Springer;Society for Computational Economics, vol. 29(3), pages 283-312, May.
    13. Xun Li & Ping Lin & Xue-Cheng Tai & Jinghui Zhou, 2015. "Pricing Two-asset Options under Exponential L\'evy Model Using a Finite Element Method," Papers 1511.04950, arXiv.org.
    14. Edie Miglio & Carlo Sgarra, 2008. "A Finite Element Framework for Option Pricing with the Bates Model," Papers 0812.3083, arXiv.org.
    15. Yang, Yi & Huang, Jin & Wang, Yifei & Deng, Ting & Li, Hu, 2023. "Fast Q1 finite element for two-dimensional integral fractional Laplacian," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    16. Zhang, Le & Schmidt, Wolfgang M., 2016. "An approximation of small-time probability density functions in a general jump diffusion model," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 741-758.
    17. Adrien Genin & Peter Tankov, 2016. "Optimal importance sampling for L\'evy Processes," Papers 1608.04621, arXiv.org.
    18. Cetin, Umut, 2019. "Linear inverse problems for Markov processes and their regularisation," LSE Research Online Documents on Economics 102633, London School of Economics and Political Science, LSE Library.
    19. E. Benhamou & E. Gobet & M. Miri, 2009. "Smart expansion and fast calibration for jump diffusions," Finance and Stochastics, Springer, vol. 13(4), pages 563-589, September.
    20. Cartea, Álvaro & del-Castillo-Negrete, Diego, 2007. "Fractional diffusion models of option prices in markets with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 749-763.

    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:126:y:2016:i:10:p:3202-3234. 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.