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General Freidlin-Wentzell Large Deviations and positive diffusions

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  • Baldi, P.
  • Caramellino, L.

Abstract

We prove Freidlin-Wentzell Large Deviation estimates under rather minimal assumptions. This allows one to derive Wentzell-Freidlin Large Deviation estimates for diffusions on the positive half line with coefficients that are neither bounded nor Lipschitz continuous. This applies to models of interest in Finance, i.e. the CIR and the CEV models, which are positive diffusion processes whose diffusion coefficient is only Hölder continuous.

Suggested Citation

  • Baldi, P. & Caramellino, L., 2011. "General Freidlin-Wentzell Large Deviations and positive diffusions," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1218-1229, August.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1218-1229
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    References listed on IDEAS

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    1. Robertson, Scott, 2010. "Sample path Large Deviations and optimal importance sampling for stochastic volatility models," Stochastic Processes and their Applications, Elsevier, vol. 120(1), pages 66-83, January.
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    Cited by:

    1. Louis-Pierre Arguin & Nien-Lin Liu & Tai-Ho Wang, 2017. "Most-likely-path in Asian option pricing under local volatility models," Papers 1706.02408, arXiv.org, revised Aug 2018.
    2. Archil Gulisashvili, 2020. "Time-inhomogeneous Gaussian stochastic volatility models: Large deviations and super roughness," Papers 2002.05143, arXiv.org, revised Dec 2020.
    3. Gulisashvili, Archil, 2020. "Gaussian stochastic volatility models: Scaling regimes, large deviations, and moment explosions," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3648-3686.
    4. Cai, Yujie & Wang, Shaochen, 2015. "Central limit theorem and moderate deviation principle for CKLS model with small random perturbation," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 6-11.
    5. Archil Gulisashvili, 2020. "Large deviation principles for stochastic volatility models with reflection and three faces of the Stein and Stein model," Papers 2006.15431, arXiv.org.
    6. Archil Gulisashvili, 2018. "Gaussian stochastic volatility models: Scaling regimes, large deviations, and moment explosions," Papers 1808.00421, arXiv.org, revised Jun 2019.
    7. Gulisashvili, Archil, 2021. "Time-inhomogeneous Gaussian stochastic volatility models: Large deviations and super roughness," Stochastic Processes and their Applications, Elsevier, vol. 139(C), pages 37-79.
    8. Louis-Pierre Arguin & Nien-Lin Liu & Tai-Ho Wang, 2018. "Most-Likely-Path In Asian Option Pricing Under Local Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-32, August.
    9. Dong, Zhao & Gu, Fan & Li, Liang, 2024. "The concentration of zero-noise limits of invariant measures for stochastic dynamical systems," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    10. Dan Pirjol & Jing Wang & Lingjiong Zhu, 2017. "Short Maturity Forward Start Asian Options in Local Volatility Models," Papers 1710.03160, arXiv.org.
    11. Marc Geha & Antoine Jacquier & Zan Zuric, 2021. "Large and moderate deviations for importance sampling in the Heston model," Papers 2111.00348, arXiv.org.
    12. Dan Pirjol & Lingjiong Zhu, 2017. "Short Maturity Asian Options for the CEV Model," Papers 1702.03382, arXiv.org.
    13. Archil Gulisashvili, 2022. "Multivariate Stochastic Volatility Models and Large Deviation Principles," Papers 2203.09015, arXiv.org, revised Nov 2022.

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