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Zhang L2 -Regularity for the solutions of Forward Backward Doubly Stochastic Differential Equations under globally Lipschitz continuous assumptions

Author

Listed:
  • Achref Bachouch

    (UiO - University of Oslo)

  • Anis Matoussi

    (Département de Mathématiques [Le Mans] - UM - Le Mans Université, IRA - Institut du Risque et de l'Assurance, Le Mans)

Abstract

We prove an L2-regularity result for the solutions of Forward Backward Doubly Stochastic Differentiel Equations (F-BDSDEs in short) under globally Lipschitz continuous assumptions on the coefficients. Therefore, we extend the well known regularity results established by Zhang (2004) for Forward Backward Stochastic Differential Equations (F-BSDEs in short) to the doubly stochastic framework. To this end, we prove (by Malliavin calculus) a representation result for the martingale component of the solution of the F-BDSDE under the assumption that the coefficients are continuous in time and continuously differentiable in space with bounded partial derivatives. As an (important) application of our L2-regularity result, we derive the rate of convergence in time for the (Euler time discretization based) numerical scheme for F-BDSDEs proposed by Bachouch et al.(2016) under only globally Lipschitz continuous assumptions.

Suggested Citation

  • Achref Bachouch & Anis Matoussi, 2017. "Zhang L2 -Regularity for the solutions of Forward Backward Doubly Stochastic Differential Equations under globally Lipschitz continuous assumptions," Working Papers hal-01548712, HAL.
    • Handle: RePEc:hal:wpaper:hal-01548712
    Note: View the original document on HAL open archive server: https://hal.science/hal-01548712v1
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    More about this item

    Keywords

    Forward Backward Doubly Stochastic Differential Equations; L2 -regularity; Malliavin calculus; representation result; numerical scheme; rate of convergence;
    All these keywords.

    JEL classification:

    • L2 - Industrial Organization - - Firm Objectives, Organization, and Behavior

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