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Cubature on C^1 space


  • Gabriel Turinici

    () (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique)


We explore in this paper cubature formulas over the space of functions having a first continuous derivative, i.e., C^1. We show that known cubature formulas are not optimal in this case and explain what is the origin of the loss of optimality and how to construct optimal ones; to illustrate we give cubature formulas up to (including) order 9.

Suggested Citation

  • Gabriel Turinici, 2013. "Cubature on C^1 space," Post-Print hal-00660875, HAL.
  • Handle: RePEc:hal:journl:hal-00660875
    DOI: 10.1007/978-3-0348-0631-2_9
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    References listed on IDEAS

    1. Esteban Moro & Javier Vicente & Luis G. Moyano & Austin Gerig & J. Doyne Farmer & Gabriella Vaglica & Fabrizio Lillo & Rosario N. Mantegna, 2009. "Market impact and trading profile of large trading orders in stock markets," Papers 0908.0202,
    2. Aurélien Alfonsi & Alexander Schied, 2010. "Optimal trade execution and absence of price manipulations in limit order book models," Post-Print hal-00397652, HAL.
    3. Aur'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756,, revised Feb 2010.
    4. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    5. Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
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    Cubature Formulae; Stochastic Analysis; Chen Series; cubature on in nite dimensional space; Cubature Wiener;

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