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Efficient importance sampling for events of moderate deviations with applications

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  • Cheng-Der Fuh

Abstract

We propose a method for finding the alternative distribution in importance sampling. The alternative distribution is optimal in the sense that the asymptotic variance is minimised for estimating tail probabilities of asymptotically normal statistics. Our contribution to importance sampling is three-fold. To begin with, we obtain an explicit expression for the mean of the optimal alternative distribution and the expression motivates a recursive approximation algorithm. Secondly, a new multi-dimensional exponential tilting formula is presented. Lastly, a conservative estimator of the variance is given to facilitate a quick comparison among different stratified sampling schemes in conjunction with importance sampling. Several numerical examples illustrating the efficacy of the proposed method are also included. These results indicate that the proposed method is considerably more efficient than the method based on large deviations theory and the efficiency gain is more significant in higher dimensions. Copyright Biometrika Trust 2004, Oxford University Press.

Suggested Citation

  • Cheng-Der Fuh, 2004. "Efficient importance sampling for events of moderate deviations with applications," Biometrika, Biometrika Trust, vol. 91(2), pages 471-490, June.
    • Handle: RePEc:oup:biomet:v:91:y:2004:i:2:p:471-490
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    Citations

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    Cited by:

    1. Huei-Wen Teng & Cheng-Der Fuh & Chun-Chieh Chen, 2016. "On an automatic and optimal importance sampling approach with applications in finance," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1259-1271, August.
    2. Cheng-Der Fuh & Yanwei Jia & Steven Kou, 2023. "A General Framework for Importance Sampling with Latent Markov Processes," Papers 2311.12330, arXiv.org.
    3. Cheng-Der Fuh & Huei-Wen Teng & Ren-Her Wang, 2018. "Efficient Simulation of Value-at-Risk Under a Jump Diffusion Model: A New Method for Moderate Deviation Events," Computational Economics, Springer;Society for Computational Economics, vol. 51(4), pages 973-990, April.
    4. Cheng-Der Fuh & Inchi Hu & Ya-Hui Hsu & Ren-Her Wang, 2011. "Efficient Simulation of Value at Risk with Heavy-Tailed Risk Factors," Operations Research, INFORMS, vol. 59(6), pages 1395-1406, December.
    5. Cheng-Der Fuh & Chuan-Ju Wang, 2017. "Efficient Exponential Tilting for Portfolio Credit Risk," Papers 1711.03744, arXiv.org, revised Apr 2019.
    6. Shih-Kuei Lin & Ren-Her Wang & Cheng-Der Fuh, 2006. "Risk Management for Linear and Non-Linear Assets: A Bootstrap Method with Importance Resampling to Evaluate Value-at-Risk," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(3), pages 261-295, September.

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