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Stochastic Approximation with Averaging Innovation Applied to Finance

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.
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https://hal.archives-ouvertes.fr/hal-00504644
Contributor : Sophie Laruelle <>
Submitted on : Monday, September 10, 2012 - 7:45:45 PM
Last modification on : Wednesday, December 9, 2020 - 3:06:10 PM
Long-term archiving on: : Tuesday, December 11, 2012 - 3:43:27 AM

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  • HAL Id : hal-00504644, version 4
  • ARXIV : 1007.3578

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Sophie Laruelle, Gilles Pagès. Stochastic Approximation with Averaging Innovation Applied to Finance. 2012. ⟨hal-00504644v4⟩

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