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A Review of Recent Results on Approximation of Solutions of Stochastic Differential Equations

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Stochastic Analysis with Financial Applications

Part of the book series: Progress in Probability ((PRPR,volume 65))

Abstract

In this article, we give a brief review of some recent results concerning the study of the Euler-Maruyama scheme and its high-order extensions. These numerical schemes are used to approximate solutions of stochastic differential equations, which enables to approximate various important quantities including solutions of partial differential equations. Some have been implemented in Premia [56]. In this article we mainly consider results about weak approximation, the most important for financial applications.

Mathematics Subject Classification (2000). 60H35, 65C05,65C30.

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Author information

Authors and Affiliations

  1. Université Paris-Est, CERMICS Project team MathFi ENPC-INRIA-UMLV, 6 et 8, avenue Blaise Pascal Cité Descartes – Champs-sur-Marne, F-77455, Marne-la-Vallée Cedex 2, France

    Benjamin Jourdain

  2. Japan Science and Technology Agency Department of Mathematical Sciences, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu Shiga, 525-8577, Japan

    Arturo Kohatsu-Higa

Authors
  1. Benjamin Jourdain
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  2. Arturo Kohatsu-Higa
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Correspondence to Benjamin Jourdain .

Editor information

Editors and Affiliations

  1. Japan Science and Technology Agency, Department of Mathematical Sciences, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga, 525-8577, Japan

    Arturo Kohatsu-Higa

  2. Division of Mathematical Sciences, Nanyang Technological University, SPMS-MAS-05-43, 21 Nanyang Link, Singapore, 637371, Singapore

    Nicolas Privault

  3. Department of Mathematics, National Central University, No.300, Zhongda Rd., Zhongli City, 320, Taiwan R.O.C.

    Shuenn-Jyi Sheu

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Jourdain, B., Kohatsu-Higa, A. (2011). A Review of Recent Results on Approximation of Solutions of Stochastic Differential Equations. In: Kohatsu-Higa, A., Privault, N., Sheu, SJ. (eds) Stochastic Analysis with Financial Applications. Progress in Probability, vol 65. Springer, Basel. https://doi.org/10.1007/978-3-0348-0097-6_9

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