Template-Type: ReDIF-Paper 1.0
Author-Name:  Leonidas Sandoval Junior
Author-Name-First: Leonidas
Author-Name-Last: Sandoval Junior
Author-Name:  Adriana Bruscato
Author-Name-First: Adriana
Author-Name-Last: Bruscato
Author-Name: Maria Kelly Venezuela
Author-Name-First: Maria Kelly
Author-Name-Last: Venezuela
Title: Weak Approximations for Wiener Functionals
Abstract:  In this paper we introduce a simple space-filtration discretization scheme on Wiener space which allows us to study weak decompositions and smooth explicit approximations for a large class of Wiener functionals. We show that any Wiener functional has an underlying robust semimartingale skeleton which under mild conditions converges to it. The discretization is given in terms of discrete-jumping filtrations which allow us to approximate non-smooth processes by means of a stochastic derivative operator on the Wiener space. As a by-product, we provide a robust semimartingale approximation for weak Dirichlet-type processes.
The underlying semimartingale skeleton is intrinsically constructed in such way that all the relevant structure is amenable to a robust numerical scheme.
In order to illustrate the results, we provide an easily implementable approximation scheme for the classical Clark-Ocone formula in full generality. Unlike in previous works, our methodology does not assume an underlying Markovian structure and does not require Malliavin weights. We conclude by proposing a method that enables us to compute optimal stopping times for possibly non-Markovian systems arising e.g. from the fractional Brownian motion.
Length:  26 pages
Creation-Date:  2012
Order-URL: https://repositorio.insper.edu.br/handle/11224/5915
File-URL: https://repositorio.insper.edu.br/handle/11224/5915
File-Format: text/html
File-Function: Full text
Number: 162
Handle: RePEc:aap:wpaper:162