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A second-order discretization for forward-backward SDEs using local approximations with Malliavin calculus

Author

Listed:
  • Naito Riu

    (Asset Management One Co., Ltd., Tokyo, Japan)

  • Yamada Toshihiro

    (Hitotsubashi University, Tokyo, Japan)

Abstract

The paper proposes a new second-order discretization method for forward-backward stochastic differential equations. The method is given by an algorithm with polynomials of Brownian motions where the local approximations using Malliavin calculus play a role. For the implementation, we introduce a new least squares Monte Carlo method for the scheme. A numerical example is illustrated to check the effectiveness.

Suggested Citation

  • Naito Riu & Yamada Toshihiro, 2019. "A second-order discretization for forward-backward SDEs using local approximations with Malliavin calculus," Monte Carlo Methods and Applications, De Gruyter, vol. 25(4), pages 341-361, December.
    • Handle: RePEc:bpj:mcmeap:v:25:y:2019:i:4:p:341-361:n:6
    DOI: 10.1515/mcma-2019-2053
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    References listed on IDEAS

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    1. Fujii, Masaaki & Takahashi, Akihiko, 2019. "Solving backward stochastic differential equations with quadratic-growth drivers by connecting the short-term expansions," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1492-1532.
    2. Gobet, Emmanuel & Labart, Céline, 2007. "Error expansion for the discretization of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 803-829, July.
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