Stochastic approximation with averaging innovation applied to Finance

Laruelle Sophie () and Pagès Gilles ()
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Laruelle Sophie: Laboratoire de Probabilités et Modèles aléatoires, UMR 7599, UPMC, case 188, 4, pl. Jussieu, F-75252 Paris Cedex 5, France
Pagès Gilles: Laboratoire de Probabilités et Modèles aléatoires, UMR 7599, UPMC, case 188, 4, pl. Jussieu, F-75252 Paris Cedex 5, France

Monte Carlo Methods and Applications, 2012, vol. 18, issue 1, 1-51

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 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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DOI: 10.1515/mcma-2011-0018

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