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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 based on a notion of pathwise functional derivative 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. The approximation and the proof of its convergence are based on the Functional Ito calculus, and require neither the Markov property, nor any differentiability conditions on the coefficients of the stochastic differential equations involved.
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https://hal.archives-ouvertes.fr/hal-01099787
Contributor : Rama Cont <>
Submitted on : Friday, January 16, 2015 - 12:33:33 PM
Last modification on : Saturday, March 28, 2020 - 2:14:58 AM
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  • HAL Id : hal-01099787, version 2
  • ARXIV : 1501.00383

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Rama Cont, Yi Lu. Weak approximation of martingale representations. 2014. ⟨hal-01099787v2⟩

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