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Numerical computation for backward doubly SDEs with random terminal time

Author

Listed:
  • Matoussi Anis

    (University of Maine, Risk and Insurance Institute of Le Mans, Laboratoire Manceau de Mathématiques, Avenue Olivier Messiaen, France)

  • Sabbagh Wissal

    (University of Maine, Risk and Insurance Institute of Le Mans, Laboratoire Manceau de Mathématiques, Avenue Olivier Messiaen, France)

Abstract

In this article, we are interested in solving numerically backward doubly stochastic differential equations (BDSDEs) with random terminal time τ. The main motivations are giving a probabilistic representation of the Sobolev’s solution of Dirichlet problem for semilinear SPDEs and providing the numerical scheme for such SPDEs. Thus, we study the strong approximation of this class of BDSDEs when τ is the first exit time of a forward SDE from a cylindrical domain. Euler schemes and bounds for the discrete-time approximation error are provided.

Suggested Citation

  • Matoussi Anis & Sabbagh Wissal, 2016. "Numerical computation for backward doubly SDEs with random terminal time," Monte Carlo Methods and Applications, De Gruyter, vol. 22(3), pages 229-258, September.
    • Handle: RePEc:bpj:mcmeap:v:22:y:2016:i:3:p:229-258:n:3
    DOI: 10.1515/mcma-2016-0111
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    References listed on IDEAS

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    1. Gobet, Emmanuel, 2000. "Weak approximation of killed diffusion using Euler schemes," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 167-197, June.
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    8. Crisan, D. & Manolarakis, K. & Touzi, N., 2010. "On the Monte Carlo simulation of BSDEs: An improvement on the Malliavin weights," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1133-1158, July.
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