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

Achref Bachouch and Anis Matoussi ()
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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

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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.

Keywords: Forward Backward Doubly Stochastic Differential Equations; L2 -regularity; Malliavin calculus; representation result; numerical scheme; rate of convergence (search for similar items in EconPapers)
Date: 2017-06-27
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