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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.
Keywords.: Stochastic approximation; sequence with low discrepancy; quasi-Monte Carlo; -mixing process; Gàl–Koksma theorem; stationary process; ergodic control; two-armed bandit algorithm; calibration; optimal asset allocation; Value-at-Risk; Conditional Value-at-Risk
Received: 2011-03-23
Accepted: 2011-11-30
Published Online: 2012-02-29
Published in Print: 2012-March
© 2012 by Walter de Gruyter Berlin Boston
