Weak approximation of martingale representations

Rama Cont and Yi Lu

Stochastic Processes and their Applications, 2016, vol. 126, issue 3, 857-882

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.

Keywords: Martingale representation; Semimartingale; Functional calculus; Functional Ito calculus; Clark–Ocone formula; Malliavin calculus; Stochastic differential equations; Euler approximation (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.spa.2015.10.002

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