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Weak approximation of martingale representations

Abstract : We present a systematic method for computing explicit approximations to martingale representations for a large class of Brownian functionals. The approximations are obtained by computing a directional derivative of the weak Euler scheme and yield a consistent estimator for the integrand in the martingale representation formula for any square-integrable functional of the solution of an SDE with path-dependent coefficients. Explicit convergence rates are derived for functionals which are Lipschitz-continuous in the supremum norm. Our results require neither the Markov property, nor any differentiability conditions on the functional or the coefficients of the stochastic differential equations involved.
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Submitted on : Tuesday, February 2, 2016 - 12:02:21 PM
Last modification on : Friday, March 27, 2020 - 3:13:17 AM

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R. Cont, Y. Lu. Weak approximation of martingale representations. Stochastic Processes and their Applications, Elsevier, 2016, 126 (3), pp.857-882. ⟨10.1016/⟩. ⟨hal-01266220⟩



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