Stochastic Approximation with Averaging Innovation Applied to Finance

Details Stochastic Approximation with Averaging Innovation Applied to Finance Stochastic Approximation with Averaging Innovation Applied to Finance

2010-07-21

arxiv.org/abs/1007.3578v3

Mathematics

Probability

Scientific paper

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.

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