Article Dans Une Revue Monte Carlo Methods and Applications Année : 2012

Stochastic Approximation with Averaging Innovation Applied to Finance

Résumé

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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Dates et versions

hal-00504644 , version 1 (20-07-2010)
hal-00504644 , version 2 (23-03-2011)
hal-00504644 , version 3 (05-12-2011)
hal-00504644 , version 4 (10-09-2012)

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Sophie Laruelle, Gilles Pagès. Stochastic Approximation with Averaging Innovation Applied to Finance. Monte Carlo Methods and Applications, 2012, 18 (1), pp.1-52. ⟨hal-00504644v4⟩
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