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A Monte Carlo method for backward stochastic differential equations with Hermite martingales

Author

Listed:
  • Pelsser Antoon

    (Deptartment of Quantitative Economics, Maastricht University and Netspar, Maastricht, Netherlands)

  • Gnameho Kossi

    (Deptartment of Quantitative Economics, Maastricht University, Maastricht, Netherlands)

Abstract

Backward stochastic differential equations (BSDEs) appear in many problems in stochastic optimal control theory, mathematical finance, insurance and economics. This work deals with the numerical approximation of the class of Markovian BSDEs where the terminal condition is a functional of a Brownian motion. Using Hermite martingales, we show that the problem of solving a BSDE is identical to solving a countable infinite-dimensional system of ordinary differential equations (ODEs). The family of ODEs belongs to the class of stiff ODEs, where the associated functional is one-sided Lipschitz. On this basis, we derive a numerical scheme and provide numerical applications.

Suggested Citation

  • Pelsser Antoon & Gnameho Kossi, 2019. "A Monte Carlo method for backward stochastic differential equations with Hermite martingales," Monte Carlo Methods and Applications, De Gruyter, vol. 25(1), pages 37-60, March.
    • Handle: RePEc:bpj:mcmeap:v:25:y:2019:i:1:p:37-60:n:2
    DOI: 10.1515/mcma-2019-2028
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    References listed on IDEAS

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    1. Masaaki Fujii & Akihiko Takahashi, 2012. "ANALYTICAL APPROXIMATION FOR NON-LINEAR FBSDEs WITH PERTURBATION SCHEME," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(05), pages 1-24.
    2. Gong, Benxue & Rui, Hongxing, 2015. "One order numerical scheme for forward–backward stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 220-231.
    3. Masaaki Fujii & Akihiko Takahashi, 2011. "Analytical Approximation for Non-linear FBSDEs with Perturbation Scheme," Papers 1106.0123, arXiv.org, revised Jan 2012.
    4. repec:dau:papers:123456789/7101 is not listed on IDEAS
    5. Bouchard, Bruno & Touzi, Nizar, 2004. "Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 175-206, June.
    6. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    7. Masaaki Fujii, Akihiko Takahashi, 2012. "Analytical Approximation for Non-linear FBSDEs with Perturbation Scheme," CARF F-Series CARF-F-269, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
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    More about this item

    Keywords

    Regression; BSDE; ODE; Hermite polynomials; martingale; 65C05; 65C40; 60H10;
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