IDEAS home Printed from https://ideas.repec.org/p/mse/wpsorb/b04080.html
   My bibliography  Save this paper

On an extension of the Hilbertian central limit theorem to Dirichlet forms

Author

Listed:
  • Christophe Chorro

    (CERMSEM et CERMICS)

Abstract

In a recent paper, Bouleau provides a new tool, based on the language of Dirichlet forms, to study the errors propagation and reinforce the historical approach of Gauss. As the classical central limit theorem is a theoric justification of the employment of normal laws in statistics, the aim of this article is to underline the importance of certain classes of error structures by asymptotic arguments. Thus, we extend the notions of independence and convergence in distribution for random variables in order to prove a refinement of the hilbertian central limit theorem that highlights the fundamental role of the error structures of the Ornstein-Ulhenbeck type

Suggested Citation

  • Christophe Chorro, 2004. "On an extension of the Hilbertian central limit theorem to Dirichlet forms," Cahiers de la Maison des Sciences Economiques b04080, Université Panthéon-Sorbonne (Paris 1).
    • Handle: RePEc:mse:wpsorb:b04080
    as

    Download full text from publisher

    File URL: ftp://mse.univ-paris1.fr/pub/mse/cahiers2004/B04080.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
    2. Nicolas Bouleau, 2003. "Error Calculus and Path Sensitivity in Financial Models," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 115-134, 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. Christophe Chorro, 2005. "Convergence en loi de Dirichlet de certaines intégrales stochastiques," Cahiers de la Maison des Sciences Economiques b05036, Université Panthéon-Sorbonne (Paris 1).
    2. Christophe Chorro, 2005. "Convergence en loi de Dirichlet de certaines intégrales stochastiques," Post-Print halshs-00194673, HAL.

    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. Maria Elvira Mancino & Simona Sanfelici, 2020. "Nonparametric Malliavin–Monte Carlo Computation of Hedging Greeks," Risks, MDPI, vol. 8(4), pages 1-17, November.
    2. Elisa Alòs & Christian-Olivier Ewald, 2005. "A note on the Malliavin differentiability of the Heston volatility," Economics Working Papers 880, Department of Economics and Business, Universitat Pompeu Fabra.
    3. Anne Laure Bronstein & Gilles Pagès & Jacques Portès, 2013. "Multi-asset American Options and Parallel Quantization," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 547-561, September.
    4. repec:pri:metric:wp033_2012_hansen_borovicka_hendricks_scheinkman_risk%20price%20dynamics. is not listed on IDEAS
    5. Jakša Cvitanić & Jin Ma & Jianfeng Zhang, 2003. "Efficient Computation of Hedging Portfolios for Options with Discontinuous Payoffs," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 135-151, January.
    6. 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.
    7. Arturo Kohatsu-Higa & Miquel Montero, 2001. "An application of Malliavin Calculus to Finance," Papers cond-mat/0111563, arXiv.org.
    8. Jérôme Detemple & René Garcia & Marcel Rindisbacher, 2005. "Asymptotic Properties of Monte Carlo Estimators of Derivatives," Management Science, INFORMS, vol. 51(11), pages 1657-1675, November.
    9. El-Khatib, Youssef & Abdulnasser, Hatemi-J, 2011. "On the calculation of price sensitivities with jump-diffusion structure," MPRA Paper 30596, University Library of Munich, Germany.
    10. Anselm Hudde & Ludger Rüschendorf, 2023. "European and Asian Greeks for Exponential Lévy Processes," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-24, March.
    11. Aintablian, Sebouh & Khoury, Wissam El, 2017. "A simulation on the presence of competing bidders in mergers and acquisitions," Finance Research Letters, Elsevier, vol. 22(C), pages 233-243.
    12. Coffie, Emmanuel & Duedahl, Sindre & Proske, Frank, 2023. "Sensitivity analysis with respect to a stochastic stock price model with rough volatility via a Bismut–Elworthy–Li formula for singular SDEs," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 156-195.
    13. Dan Pirjol & Lingjiong Zhu, 2023. "Sensitivities of Asian options in the Black-Scholes model," Papers 2301.06460, arXiv.org.
    14. Ma, Jin & Zhang, Jianfeng, 2005. "Representations and regularities for solutions to BSDEs with reflections," Stochastic Processes and their Applications, Elsevier, vol. 115(4), pages 539-569, April.
    15. Hyungbin Park, 2018. "Sensitivity analysis of long-term cash flows," Finance and Stochastics, Springer, vol. 22(4), pages 773-825, October.
    16. Bouchard, Bruno & Chassagneux, Jean-François, 2008. "Discrete-time approximation for continuously and discretely reflected BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2269-2293, December.
    17. Cont, Rama & Lu, Yi, 2016. "Weak approximation of martingale representations," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 857-882.
    18. Arturo Kohatsu & Roger Pettersson, 2002. "Variance reduction methods for simulation of densities on Wiener space," Economics Working Papers 597, Department of Economics and Business, Universitat Pompeu Fabra.
    19. Jaroslav Borovička & Mark Hendricks & José A. Scheinkman, 2011. "Risk-Price Dynamics," Journal of Financial Econometrics, Oxford University Press, vol. 9(1), pages 3-65, Winter.
      • Jaroslav Borovička & Lars Peter Hansen & Mark Hendricks & José A. Scheinkman, 2009. "Risk Price Dynamics," NBER Working Papers 15506, National Bureau of Economic Research, Inc.
      • Jaroslav Borovicka & Lars Peter Hansen & Mark Hendricks & Jose A. Scheinkman, 2009. "Risk Price Dynamics," Working Papers 1393, Princeton University, Department of Economics, Econometric Research Program..
    20. Mascagni Michael & Qiu Yue & Hin Lin-Yee, 2014. "High performance computing in quantitative finance: A review from the pseudo-random number generator perspective," Monte Carlo Methods and Applications, De Gruyter, vol. 20(2), pages 101-120, June.
    21. Frazier, David T. & Oka, Tatsushi & Zhu, Dan, 2019. "Indirect inference with a non-smooth criterion function," Journal of Econometrics, Elsevier, vol. 212(2), pages 623-645.

    More about this item

    Keywords

    Error; sensitivity; Dirichlet forms; squared field operator; vectorial domain; central limit theorem;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:mse:wpsorb:b04080. 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: Lucie Label (email available below). General contact details of provider: https://edirc.repec.org/data/msep1fr.html .

    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.