Weak approximation of martingale representations

R. Cont (1) , Y. Lu (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Domaines: Probabilités [math.PR]

R. Cont, Y. Lu. Weak approximation of martingale representations. Stochastic Processes and their Applications, 2016, 126 (3), pp.857-882. ⟨10.1016/j.spa.2015.10.002⟩. ⟨hal-01266220⟩