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Stochastic approximation with averaging innovation applied to Finance

Author

Listed:
  • 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)

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.

Suggested Citation

  • Laruelle Sophie & Pagès Gilles, 2012. "Stochastic approximation with averaging innovation applied to Finance," Monte Carlo Methods and Applications, De Gruyter, vol. 18(1), pages 1-51, January.
    • Handle: RePEc:bpj:mcmeap:v:18:y:2012:i:1:p:1-51:n:1
    DOI: 10.1515/mcma-2011-0018
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    References listed on IDEAS

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    1. Lemaire, Vincent, 2007. "An adaptive scheme for the approximation of dissipative systems," Stochastic Processes and their Applications, Elsevier, vol. 117(10), pages 1491-1518, October.
    2. Bardou O. & Frikha N. & Pagès G., 2009. "Computing VaR and CVaR using stochastic approximation and adaptive unconstrained importance sampling," Monte Carlo Methods and Applications, De Gruyter, vol. 15(3), pages 173-210, January.
    3. Arne Løkka & Mihail Zervos, 2011. "A Model For The Long-Term Optimal Capacity Level Of An Investment Project," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(02), pages 187-196.
    4. Gourieroux, C. & Jasiak, J. & Sufana, R., 2009. "The Wishart Autoregressive process of multivariate stochastic volatility," Journal of Econometrics, Elsevier, vol. 150(2), pages 167-181, June.
    5. Douc, R. & Fort, G. & Moulines, E. & Priouret, P., 2009. "Forgetting the initial distribution for Hidden Markov Models," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1235-1256, April.
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    Cited by:

    1. Zsolt Nika & Mikl'os R'asonyi, 2019. "Learning Threshold-Type Investment Strategies with Stochastic Gradient Method," Papers 1907.02457, arXiv.org.
    2. Gadat, Sébastien & Costa, Manon & Huang, Lorick, 2022. "CV@R penalized portfolio optimization with biased stochastic mirror descent," TSE Working Papers 22-1342, Toulouse School of Economics (TSE), revised Nov 2023.
    3. Miklos Rasonyi & Kinga Tikosi, 2020. "Convergence of the Kiefer-Wolfowitz algorithm in the presence of discontinuities," Papers 2007.14069, arXiv.org, revised Sep 2021.

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