IDEAS home Printed from https://ideas.repec.org/a/bpj/mcmeap/v18y2012i1p1-51n1.html
   My bibliography  Save this article

Stochastic approximation with averaging innovation applied to Finance

Author

Listed:
  • Laruelle Sophie

    (Laboratoire de Probabilités et Modèles aléatoires, UMR 7599, UPMC, case 188, 4, pl. Jussieu, F-75252 Paris Cedex 5, France)

  • Pagès Gilles

    (Laboratoire de Probabilités et Modèles aléatoires, UMR 7599, UPMC, case 188, 4, pl. Jussieu, F-75252 Paris Cedex 5, France)

Abstract

The aim of the paper is to establish a convergence theorem for multi-dimensional stochastic approximation when the “innovations” satisfy some “light” averaging properties in the presence of a pathwise Lyapunov function. These averaging assumptions allow us to unify apparently remote frameworks where the innovations are simulated (possibly deterministic like in quasi-Monte Carlo simulation) or exogenous (like market data) with ergodic properties. We propose several fields of applications and illustrate our results on five examples mainly motivated by finance.

Suggested Citation

  • Laruelle Sophie & Pagès Gilles, 2012. "Stochastic approximation with averaging innovation applied to Finance," Monte Carlo Methods and Applications, De Gruyter, vol. 18(1), pages 1-51, January.
    • Handle: RePEc:bpj:mcmeap:v:18:y:2012:i:1:p:1-51:n:1
    DOI: 10.1515/mcma-2011-0018
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/mcma-2011-0018
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/mcma-2011-0018?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. Douc, R. & Fort, G. & Moulines, E. & Priouret, P., 2009. "Forgetting the initial distribution for Hidden Markov Models," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1235-1256, April.
    2. Arne Løkka & Mihail Zervos, 2011. "A Model For The Long-Term Optimal Capacity Level Of An Investment Project," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(02), pages 187-196.
    3. Gourieroux, C. & Jasiak, J. & Sufana, R., 2009. "The Wishart Autoregressive process of multivariate stochastic volatility," Journal of Econometrics, Elsevier, vol. 150(2), pages 167-181, June.
    4. Lemaire, Vincent, 2007. "An adaptive scheme for the approximation of dissipative systems," Stochastic Processes and their Applications, Elsevier, vol. 117(10), pages 1491-1518, October.
    5. Bardou O. & Frikha N. & Pagès G., 2009. "Computing VaR and CVaR using stochastic approximation and adaptive unconstrained importance sampling," Monte Carlo Methods and Applications, De Gruyter, vol. 15(3), pages 173-210, January.
    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. Zsolt Nika & Mikl'os R'asonyi, 2019. "Learning Threshold-Type Investment Strategies with Stochastic Gradient Method," Papers 1907.02457, arXiv.org.
    2. Gadat, Sébastien & Costa, Manon & Huang, Lorick, 2022. "CV@R penalized portfolio optimization with biased stochastic mirror descent," TSE Working Papers 22-1342, Toulouse School of Economics (TSE), revised Nov 2023.
    3. Miklos Rasonyi & Kinga Tikosi, 2020. "Convergence of the Kiefer-Wolfowitz algorithm in the presence of discontinuities," Papers 2007.14069, arXiv.org, revised Sep 2021.

    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. Anna Cieslak & Pavol Povala, 2016. "Information in the Term Structure of Yield Curve Volatility," Journal of Finance, American Finance Association, vol. 71(3), pages 1393-1436, June.
    2. Asai, Manabu & McAleer, Michael, 2015. "Leverage and feedback effects on multifactor Wishart stochastic volatility for option pricing," Journal of Econometrics, Elsevier, vol. 187(2), pages 436-446.
    3. Almut Veraart & Luitgard Veraart, 2012. "Stochastic volatility and stochastic leverage," Annals of Finance, Springer, vol. 8(2), pages 205-233, May.
    4. Alexander Philipov & Mark Glickman, 2006. "Factor Multivariate Stochastic Volatility via Wishart Processes," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 311-334.
    5. Asai, Manabu & McAleer, Michael, 2015. "Forecasting co-volatilities via factor models with asymmetry and long memory in realized covariance," Journal of Econometrics, Elsevier, vol. 189(2), pages 251-262.
    6. Joshua Chan & Arnaud Doucet & Roberto León-González & Rodney W. Strachan, 2018. "Multivariate Stochastic Volatility with Co-Heteroscedasticity," Working Paper series 18-38, Rimini Centre for Economic Analysis.
    7. Jin, Xin & Maheu, John M., 2016. "Bayesian semiparametric modeling of realized covariance matrices," Journal of Econometrics, Elsevier, vol. 192(1), pages 19-39.
    8. Chiu, Mei Choi & Wong, Hoi Ying & Zhao, Jing, 2015. "Commodity derivatives pricing with cointegration and stochastic covariances," European Journal of Operational Research, Elsevier, vol. 246(2), pages 476-486.
    9. Roxana Chiriac & Valeri Voev, 2011. "Modelling and forecasting multivariate realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(6), pages 922-947, September.
    10. Vassallo, Danilo & Buccheri, Giuseppe & Corsi, Fulvio, 2021. "A DCC-type approach for realized covariance modeling with score-driven dynamics," International Journal of Forecasting, Elsevier, vol. 37(2), pages 569-586.
    11. Giorgio Ferrari & Hanwu Li & Frank Riedel, 2020. "A Knightian Irreversible Investment Problem," Papers 2003.14359, arXiv.org, revised Apr 2020.
    12. Monfort, Alain & Pegoraro, Fulvio, 2012. "Asset pricing with Second-Order Esscher Transforms," Journal of Banking & Finance, Elsevier, vol. 36(6), pages 1678-1687.
    13. Xin Jin & John M. Maheu & Qiao Yang, 2019. "Bayesian parametric and semiparametric factor models for large realized covariance matrices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(5), pages 641-660, August.
    14. Pan, Zhiyuan & Xiao, Dongli & Dong, Qingma & Liu, Li, 2022. "Structural breaks, macroeconomic fundamentals and cross hedge ratio," Finance Research Letters, Elsevier, vol. 47(PA).
    15. Golosnoy, Vasyl & Gribisch, Bastian & Liesenfeld, Roman, 2015. "Intra-daily volatility spillovers in international stock markets," Journal of International Money and Finance, Elsevier, vol. 53(C), pages 95-114.
    16. Costa, Manon & Gadat, Sébastien & Bercu, Bernard, 2020. "Stochastic approximation algorithms for superquantiles estimation," TSE Working Papers 20-1142, Toulouse School of Economics (TSE).
    17. Manabu Asai & Michael McAleer, 2017. "A fractionally integrated Wishart stochastic volatility model," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 42-59, March.
    18. Gourieroux, C. & Monfort, A. & Sufana, R., 2010. "International money and stock market contingent claims," Journal of International Money and Finance, Elsevier, vol. 29(8), pages 1727-1751, December.
    19. Chiarella, Carl & Hsiao, Chih-Ying & Tô, Thuy-Duong, 2016. "Stochastic correlation and risk premia in term structure models," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 59-78.
    20. Jian, Zhihong & Deng, Pingjun & Zhu, Zhican, 2018. "High-dimensional covariance forecasting based on principal component analysis of high-frequency data," Economic Modelling, Elsevier, vol. 75(C), pages 422-431.

    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:bpj:mcmeap:v:18:y:2012:i:1:p:1-51:n:1. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyterbrill.com .

    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.