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Approximation of Non-Lipschitz SDEs by Picard Iterations

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  • Julien Baptiste
  • Julien Grepat
  • Emmanuel Lepinette

Abstract

In this article, we propose an approximation method based on Picard iterations deduced from the Doléans–Dade exponential formula. Our method allows to approximate trajectories of Markov processes in a large class, e.g., solutions to non-Lipchitz stochastic differential equation. An application to the pricing of Asian-style contingent claims in the constant elasticity of variance model is presented and compared to other methods of the literature.

Suggested Citation

  • Julien Baptiste & Julien Grepat & Emmanuel Lepinette, 2018. "Approximation of Non-Lipschitz SDEs by Picard Iterations," Applied Mathematical Finance, Taylor & Francis Journals, vol. 25(2), pages 148-179, March.
    • Handle: RePEc:taf:apmtfi:v:25:y:2018:i:2:p:148-179
    DOI: 10.1080/1350486X.2018.1507749
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    Cited by:

    1. Jürgen Geiser, 2020. "Iterative and Noniterative Splitting Methods of the Stochastic Burgers’ Equation: Theory and Application," Mathematics, MDPI, vol. 8(8), pages 1-28, July.

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