Stochastic Approximation with Averaging Innovation Applied to Finance
Probability
2012-09-12 v4
Abstract
The aim of the paper is to establish a convergence theorem for multi-dimensional stochastic approximation when the "innovations" satisfy some "light" averaging properties in the presence of a pathwise Lyapunov function. These averaging assumptions allow us to unify apparently remote frameworks where the innovations are simulated (possibly deterministic like in Quasi-Monte Carlo simulation) or exogenous (like market data) with ergodic properties. We propose several fields of applications and illustrate our results on five examples mainly motivated by Finance.
Cite
@article{arxiv.1007.3578,
title = {Stochastic Approximation with Averaging Innovation Applied to Finance},
author = {Sophie Laruelle and Gilles Pagès},
journal= {arXiv preprint arXiv:1007.3578},
year = {2012}
}