IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v125y2015i3p1009-1031.html
   My bibliography  Save this article

Asymptotic expansions for SDE’s with small multiplicative noise

Author

Listed:
  • Albeverio, Sergio
  • Smii, Boubaker

Abstract

Asymptotic expansions are derived as power series in a small coefficient entering a nonlinear multiplicative noise and a deterministic driving term in a nonlinear evolution equation. Detailed estimates on remainders are provided.

Suggested Citation

  • Albeverio, Sergio & Smii, Boubaker, 2015. "Asymptotic expansions for SDE’s with small multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 1009-1031.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:3:p:1009-1031
    DOI: 10.1016/j.spa.2014.09.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414914002142
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2014.09.009?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. Victoria Steblovskaya & Sergio Albeverio, 2002. "A model of financial market with several interacting assets. Complete market case," Finance and Stochastics, Springer, vol. 6(3), pages 383-396.
    2. Duan, Jinqiao & Yan, Jia-an, 2008. "General matrix-valued inhomogeneous linear stochastic differential equations and applications," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2361-2365, October.
    3. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    4. Masayuki Uchida & Nakahiro Yoshida, 2004. "Asymptotic Expansion for Small Diffusions Applied to Option Pricing," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 189-223, October.
    5. Albeverio, Sergio & Mastrogiacomo, Elisa & Smii, Boubaker, 2013. "Small noise asymptotic expansions for stochastic PDE’s driven by dissipative nonlinearity and Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2084-2109.
    6. Albeverio, S. & Mandrekar, V. & Rüdiger, B., 2009. "Existence of mild solutions for stochastic differential equations and semilinear equations with non-Gaussian Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 835-863, March.
    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. Liang, Song, 2016. "Stochastic Newton equation in strong potential limit," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 2913-2955.

    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. Long, Hongwei & Ma, Chunhua & Shimizu, Yasutaka, 2017. "Least squares estimators for stochastic differential equations driven by small Lévy noises," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1475-1495.
    2. Alessandro Bondi & Sergio Pulido & Simone Scotti, 2022. "The rough Hawkes Heston stochastic volatility model," Working Papers hal-03827332, HAL.
    3. Thomas Gkelsinis & Alex Karagrigoriou, 2020. "Theoretical Aspects on Measures of Directed Information with Simulations," Mathematics, MDPI, vol. 8(4), pages 1-13, April.
    4. Madan, Dilip B. & Wang, King, 2021. "The structure of financial returns," Finance Research Letters, Elsevier, vol. 40(C).
    5. Jiang, Bibo & Lu, Ye & Park, Joon Y., 2020. "Testing for Stationarity at High Frequency," Journal of Econometrics, Elsevier, vol. 215(2), pages 341-374.
    6. Hooper, Vincent J. & Ng, Kevin & Reeves, Jonathan J., 2008. "Quarterly beta forecasting: An evaluation," International Journal of Forecasting, Elsevier, vol. 24(3), pages 480-489.
    7. Dimitrios D. Thomakos & Michail S. Koubouros, 2011. "The Role of Realised Volatility in the Athens Stock Exchange," Multinational Finance Journal, Multinational Finance Journal, vol. 15(1-2), pages 87-124, March - J.
    8. Brix, Anne Floor & Lunde, Asger & Wei, Wei, 2018. "A generalized Schwartz model for energy spot prices — Estimation using a particle MCMC method," Energy Economics, Elsevier, vol. 72(C), pages 560-582.
    9. Apergis, Nicholas & Christou, Christina & Miller, Stephen M., 2014. "Country and industry convergence of equity markets: International evidence from club convergence and clustering," The North American Journal of Economics and Finance, Elsevier, vol. 29(C), pages 36-58.
    10. Todorov, Viktor & Tauchen, George & Grynkiv, Iaryna, 2014. "Volatility activity: Specification and estimation," Journal of Econometrics, Elsevier, vol. 178(P1), pages 180-193.
    11. Kumar, Rohini & Popovic, Lea, 2017. "Large deviations for multi-scale jump-diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 127(4), pages 1297-1320.
    12. Bouezmarni, Taoufik & Rombouts, Jeroen V.K., 2010. "Nonparametric density estimation for positive time series," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 245-261, February.
    13. Taufer, Emanuele & Leonenko, Nikolai, 2009. "Simulation of Lvy-driven Ornstein-Uhlenbeck processes with given marginal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2427-2437, April.
    14. Nicola Cufaro Petroni & Piergiacomo Sabino, 2020. "Tempered stable distributions and finite variation Ornstein-Uhlenbeck processes," Papers 2011.09147, arXiv.org.
    15. Ioannis Kyriakou & Panos K. Pouliasis & Nikos C. Papapostolou, 2016. "Jumps and stochastic volatility in crude oil prices and advances in average option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 16(12), pages 1859-1873, December.
    16. Chenxu Li, 2014. "Closed-Form Expansion, Conditional Expectation, and Option Valuation," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 487-516, May.
    17. Torben G. Andersen & Tim Bollerslev & Peter Christoffersen & Francis X. Diebold, 2007. "Practical Volatility and Correlation Modeling for Financial Market Risk Management," NBER Chapters, in: The Risks of Financial Institutions, pages 513-544, National Bureau of Economic Research, Inc.
    18. Fred Benth & Nils Detering, 2015. "Pricing and hedging Asian-style options on energy," Finance and Stochastics, Springer, vol. 19(4), pages 849-889, October.
    19. Douglas G. Santos & Flavio A. Ziegelmann, 2014. "Volatility Forecasting via MIDAS, HAR and their Combination: An Empirical Comparative Study for IBOVESPA," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(4), pages 284-299, July.
    20. Liang Wang & Weixuan Xia, 2022. "Power‐type derivatives for rough volatility with jumps," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(7), pages 1369-1406, July.

    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:125:y:2015:i:3:p:1009-1031. 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.