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An Approximation Scheme for Diffusion Processes Based on an Antisymmetric Calculus over Wiener Space

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  • Kazuhiro Yoshikawa

Abstract

In this paper, we show that every antisymmetric multiple stochastic (Ito’s) integral has a polynomial form of single and double ones. As an application, a new approximating scheme for the solution to a stochastic differential equation is proposed. Copyright Springer Japan 2015

Suggested Citation

  • Kazuhiro Yoshikawa, 2015. "An Approximation Scheme for Diffusion Processes Based on an Antisymmetric Calculus over Wiener Space," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(2), pages 185-207, May.
    • Handle: RePEc:kap:apfinm:v:22:y:2015:i:2:p:185-207
    DOI: 10.1007/s10690-014-9199-2
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    References listed on IDEAS

    as
    1. Syoiti Ninomiya & Nicolas Victoir, 2008. "Weak Approximation of Stochastic Differential Equations and Application to Derivative Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 107-121.
    2. Shigeo Kusuoka & Syoiti Ninomiya, 2004. "A New Simulation Method of Diffusion Processes Applied to Finance," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 11, pages 233-253, World Scientific Publishing Co. Pte. Ltd..
    3. Mariko Ninomiya & Syoiti Ninomiya, 2009. "A new higher-order weak approximation scheme for stochastic differential equations and the Runge–Kutta method," Finance and Stochastics, Springer, vol. 13(3), pages 415-443, September.
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    More about this item

    Keywords

    Stochastic area; Numerical analysis of stochastic differential equation; Fermion Fock space; G13;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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